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Polynomials

Long Answer Type

431. If α, β are the zeroes of quadratic polynomial 2x² – 3x – 5, form a quadratic polynomial whose zeroes are α² and β².

Since, α, β are the zeroes of quadratic polynomial 2x² – 3x – 5, then

straight alpha plus straight beta equals fraction numerator negative straight b over denominator straight a end fraction equals 3 over 2

and

straight alpha. straight beta equals straight c over straight a equals fraction numerator negative 5 over denominator 2 end fraction

Now,

space sum left parenthesis straight alpha plus straight beta right parenthesis space equals space straight alpha squared plus straight beta squared space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight alpha plus straight beta right parenthesis squared minus 2 αβ

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Product space left parenthesis straight alpha. space straight beta right parenthesis space equals space straight alpha squared straight beta squared space equals space left parenthesis αβ right parenthesis squared space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open parentheses fraction numerator negative 5 over denominator 2 end fraction close parentheses squared space equals space 25 over 4

So, required quadratic polynomial be

space space space space space straight K open curly brackets straight x squared minus left parenthesis straight alpha plus straight beta right parenthesis straight x plus straight alpha. space straight beta close curly brackets

straight K open curly brackets straight x squared minus open parentheses 29 over 4 close parentheses straight x plus 25 over 4 close curly brackets.

397 Views

432. If α, β are the zeroes of quadratic poly-nomial x² – 3x + 2, form a quadratic polynomial whose roots are –α and –β.

161 Views

433. If α, β are the zeroes of quadratic polynomial x² – 3x – 1, form a quadratic polynomial whose roots are

1 over straight alpha squared comma space 1 over straight beta squared.

122 Views

434. Factorize 2x⁴ + x³ – 14x² – 19x – 6 by x² + 3x + 2 and verify the division algorithm.

163 Views

Short Answer Type

435. Find all the zeroes of the polynomial x³ + 3x² – 2x – 6, if two of its zeroes are –

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1188 Views

436. Find all the zeroes of the polynomial 2a³ + x² – 6x – 3, if two of its zeroes are -

square root of 3 space and space square root of 3.

230 Views

437. If the polynomial 6x⁴+8x³ + 17x² + 21x + 7 is divided by another polynomial 3x²+ 4x +1, the remainder comes out to be (ax + b), find a and b.

2132 Views

438. If the polynomial x³ + 2x³ + 8x² + 12x + 18 is divided by another polynomial x² + 5, the remainder comes out to be px + q. Find the values of p and q.

211 Views

Long Answer Type

439. Find all the zeroes of 2x⁴ – 9x³ + 5x² + 3x– 1, if two of its zeroes are

2 plus square root of 3 space and space 2 minus square root of 3.

21071 Views

440. Find all the zeros of the polynomial x⁴ + x³ – 34x² – 4x + 120, if two of its zeroes are 2 and (–2).

2997 Views

Previous Year Papers

Test Series

Test Yourself

Long Answer Type

431. If α, β are the zeroes of quadratic polynomial 2x2 – 3x – 5, form a quadratic polynomial whose zeroes are α2 and β2.

Short Answer Type

Long Answer Type

431. If α, β are the zeroes of quadratic polynomial 2x² – 3x – 5, form a quadratic polynomial whose zeroes are α² and β².