421.Find a quadratic polynomial whose zeroes are 1 and (-3). Verify the relation between the coefficients and zeroes of the polynomial.
Let the quadratic polynomial be ax2 + bx + c, and its zeroes be α and β. Then α = 1 and β = - 3 ∴ Sum of the zeroes (α + β) = 1 + (– 3) = – 2 and, product of zeroes (a+ p) = 1 x (–3) = –3 Hence, the quadratic polynomial = x2 – (α + β) x + αβ = x2 – (– 2)x + (– 3) = x2 + 2x – 3 Now, sum of the zeroes and product of the zeroes
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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) (b)
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424.
If α and β are the zeroes of the quadratic polynomial ax2 + bx + c. Find the value of α2– β2.
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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.
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426.If α and β are the zeroes of quadratic polynomial ax2 + bx + c, then find
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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.
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428.If α and β are the zeroes of quadratic polynomial x2 + x – 2. Find the value of (α–1 + β–1).
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429.Find a quadratic polynomial when the sum and product of its zeroes respectively (i) (ii)
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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.
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Short Answer Type
(ii) 
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(b) 
