Question

If -2 and -4 are the zeroes of a quadratic polynomial whose leading coefficient is 2, then find the value of (product of zeroes $\times$ coefficient of x).

[Note: In a polynomial, the term containing the highest power of x (i.e. a_nxⁿ) is the leading term, and we call a_n the leading coefficient.]

• A. 96
• B. -96
• C. 16
• D. -16

Answer 1

The correct option is A 96

Given -2 and -4 are the zeroes of a quadratic polynomial.

So the quadratic polynomial can be written as
$f\left(x\right)=(x+2)(x+4)$
$\Rightarrow f\left(x\right)=x^2+6x+8$

Now, as the leading coefficient is 2, the quardratic polynomial will be
$f\left(x\right)=2\times (x^2+6x+8)$
$f\left(x\right)=2x^2+12x+16$

So, product of zeroes $\times$ coefficient of x
$=(-2)(-4)\times 12=96$