Question

Which quadratic polynomial can be factorized into a product of real linear factors?

• A. $2x^2-5x+9$
• B. $2x^2+4x-5$
• C. $3x^2+4x+6$
• D. $5x^2-3x+2$

Answer 1

Answer: (D)

$5x^2-3x+2$

A) $2x^2-5x+9$ ($△$ is doscriminant)

$△={(-5)}^2-4\times 2\times 9=-47<0$

$\therefore$Cannot factorized into product of real linear factors

B) $2x^2+4x-5$

$△={\left(4\right)}^2-4\left(2\right)(-5)=56>0$

$\therefore 2x^2+4x-5$ can be factorized into real linear factors.

C) $3x^2+4x+6$

$△={\left(4\right)}^2-4\left(3\right)\left(6\right)=-56<0$

$\therefore 3x^2+4x+6$ cannot be factorized into real linear factors.

D. $5x^2-3x+2$

$△={(-3)}^2-4\left(5\right)\left(2\right)=-31<0$

$\therefore 5x^2-3x+2$ cannot be factorized into real linear factors.