Question

The quadratic polynomial whose zeros are -3 and 4

x^2 – x + 12
x^2 + x + 12
x^2 – x – 12
2x^2 + 2x –24

Answer 1

Answer:-

Your Answer is Option3:- x² - x - 12.

Explanation:-

Given:-

• Zeroes of an quadratic polynomial are -3 and 4.

To Find:-

• The polynomial.

Concepts Used:-

Every quadratic polynomial is in the form,

$\\ \tt\leadsto {x}^{2} - (sum \: of \: zeroes)x + (product \:of \: zeroes).$

• Sum of zeroes = $\frac{-b}{a}.$

• Product of zeroes = $\frac{c}{a}.$

Where,

• a = Coefficient of x².

• -b = -Coefficient of x.

• c = Constant term.

So Here,

• Sum Of zeroes,

= (-3) + 4.

= -3 + 4.

= 1.

• Product Of Zeroes,

= (-3) × 4.

= -12.

Therefore the quadratic polynomial is:-

$\\ \tt\mapsto {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes) \\ \\ \tt = {x}^{2} - (1)x + ( - 12). \\ \\ \tt = {x}^{2} - x - 12.$

$\therefore$ Option 3:-

x² - x - 12 is the correct answer.