Question

Find the quadratic polynomial whose zeros are 2 and -6 (a) x2 + 4x + 12 (b) x2 – 4x – 12 (c) x2 + 4x – 12 (d) x2 – 4x + 12​

Answer 1

Answer:

a. x2+4x+12

b. x2-4x-12

c. x2+4x-12

d. x2-4x+12

If α, β, are the zeroes of the polynomial p(x) such that α+β+γ=3, αβ+βγ+γα=10, αβγ=-24, then px=?

a. x3+3x2-10x+24

b. x3-3x2+10x+24

c. x3-3x2-10x-24

d. x3+3x2+10x-24

Answer 2

ANSWER:

• Option C

EXPLANATION:

• Option 'a'

$\\ \\ = {x}^{2} + 4x + 12 \\ = {x}^{2} + 6x - 2x + 12 \\ \\ \\ quadratic \: \: equation \: \:is \: \: not \: \: possible$

• Option 'b'

$\\ \\ \\ = {x}^{2} - 4x - 12 \\ = {x}^{2} - 6x + 2x - 12 \\ = x(x - 6)2(x - 6) \\x = - 2 \: \: and \: \: 6(not \: \: equal \: \: to \: \: question)$

• Option 'c'

$\\ \\ \\ = {x}^{2} + 4x - 12 \\ = {x}^{2} + 6x - 2x - 12 \\ = x(x + 6) - 2(x + 6) \\ (x - 2)(x + 6) \\ x = 2 \: \: and \: \: - 6$

CORRECT OPTION IS HENCE 'C'