If α and β are the zeroes of the polynomial ax2 + bx + c then
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    Polynomials

    Multiple Choice QuestionsLong Answer Type

    421. Find a quadratic polynomial whose zeroes are 1 and (-3). Verify the relation between the coefficients and zeroes of the polynomial.
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    422. Find the zeroes of the quadratic polynomial 4x2 – 4x – 3 and verify the relation between the zeroes and its coefficients.
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    423. If α and β are the zeroes of the polynomial ax2 + bx + c then find
    (a)      straight alpha over straight beta plus straight beta over straight alpha             (b)   space space straight alpha squared plus straight beta squared

    Since, α and β are the zeroes of the quadratic polynomial ax2 + bx + c.
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    (a)  
                          straight alpha over straight beta plus straight beta over straight alpha equals fraction numerator straight alpha squared plus straight beta squared over denominator αβ end fraction equals space fraction numerator left parenthesis straight alpha plus straight beta right parenthesis squared minus 2 αβ over denominator αβ end fraction

                           equals fraction numerator open parentheses begin display style fraction numerator negative straight b over denominator straight a end fraction end style close parentheses squared minus 2 open parentheses begin display style straight c over straight a end style close parentheses over denominator begin display style straight c over straight a end style end fraction

                            equals fraction numerator begin display style straight b squared over straight a squared end style minus begin display style fraction numerator 2 straight c over denominator straight a end fraction end style over denominator begin display style straight c over straight a end style end fraction equals fraction numerator begin display style fraction numerator straight b squared minus 2 ac over denominator straight a squared end fraction end style over denominator begin display style straight c over straight a end style end fraction
                            
                            space space space space equals fraction numerator straight b squared minus 2 ac over denominator straight a squared end fraction cross times straight a over straight c equals fraction numerator straight b squared minus 2 ac over denominator ac end fraction.

    (b) 
                straight alpha squared plus straight beta squared space equals space left parenthesis straight alpha plus straight beta right parenthesis squared minus 2 αβ space space space space space space space space space space space space space space equals space open parentheses fraction numerator negative straight b over denominator straight a end fraction close parentheses squared minus 2 open parentheses straight c over straight a close parentheses space space space space space space space space space space space space space space equals straight b squared over straight a squared minus fraction numerator 2 straight c over denominator straight a end fraction space space space space space space space space space space space space space space space equals space fraction numerator straight b squared minus 2 ac over denominator straight a squared end fraction.

            
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    Multiple Choice QuestionsShort Answer Type

    424.

    If α and β are the zeroes of the quadratic polynomial ax2 + bx + c. Find the value of α2– β2.

    145 Views
    Answer
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    425. If α and β are the zeroes of the quadratic polynomial ax2 + bx + c, then find the value of α3 + β3.
    129 Views
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    Multiple Choice QuestionsLong Answer Type

    426. If α and β are the zeroes of quadratic polynomial ax2 + bx + c, then find straight alpha squared over straight beta plus straight beta squared over straight alpha.
    134 Views
    Answer
    427. If α and β are the zeroes of the quadratic polynomial P(x) = Kx2 + 4x + 4 such that α2 + β2 = 24, find the value of K.
    433 Views
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    Multiple Choice QuestionsShort Answer Type

    428. If α and β are the zeroes of quadratic polynomial x2 + x – 2. Find the value of (α–1 + β–1).
    107 Views
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    429. Find a quadratic polynomial when the sum and product of its zeroes respectively
    (i)  space 1 fourth comma space minus 1                  (ii)    square root of 2 comma space fraction numerator negative 1 over denominator 3 end fraction
    152 Views
    Answer

    Multiple Choice QuestionsLong Answer Type

    430. If α, β are the zeroes of the quadratic polynomial 2x2– 3x – 5, form a polynomial whose zeroes are 2α + 1 and 2β + 1.
    213 Views
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