Question

Find quadratic polynomial whose zeroes are minus 5 and 4

Answer 1

Solution :-

Zeroes are :- -5 & 4.

$\sf \: Sum \: of \: zeroes \: ( \alpha \: + \: \beta ) \: = \: - 5 \: + \: 4 \: \\ \implies \: - 1$

$\sf \: Product \: of \: zeroes \: ( \alpha \beta ) \: = \: - 5 \: \times \: 4 \: \\ \implies \: \: - 20$

$\sf \: Polynomial \: = \: a \: ( {x}^{2} \: - \: ( \alpha \: + \: \beta )x \: + \: \alpha \beta )$

$\sf \: \implies \: a \: ( {x}^{2} \: - \: ( - 1)x \: + \: ( - 20)$

$\sf \: \implies \: a \: ( {x}^{2} \: + \: x \: - \: 20)$

$\sf \: Put \: a \: = \: 1$

$\sf \: \implies \: {x}^{2} \: + \: x \: - \: 20$

$\sf \: Hence, \: the \: polynomial \: is \: :-$

$\boxed{\boxed {\sf{ {x}^{2} \: + \: x \: - \: 20}}}$

Answer 2

Answer

Zeroes = 5,4

Sum = -5 + 4 = (-1)

Product = -20

Polynomial = x^2 + x - 20