Find the quadratic polynomial sum and product of whose zeros are –1 and –20 respectively. Also find the zeroes of the polynomial so obtained.

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Solution

Q.
Find the quadratic polynomial sum and product of whose zeros are –1 and –20 respectively. Also find the zeroes of the polynomial so obtained.

Ans.
(-5,4)

Let α and β be the zeros of the quadratic polynomial.

$∴$ Sum of zeros, α + β = – 1

and product of zeros, α. β = – 20

Now, quadratic polynomial be

$x^{2} - (α + β) \cdot x + α β = x^{2} - (- 1) x - 20 = x^{2} + x - 20$

Now, for zeroes of this polynomial

$x^{2} + x - 20 = 0 \Rightarrow x^{2} + 5 x - 4 x - 20 = 0$

$\Rightarrow x (x + 5) - 4 (x + 5) = 0 \Rightarrow (x + 5) (x - 4) = 0$

$\Rightarrow x = - 5, 4$

$∴$ zeroes are – 5 and 4

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