Let x = 2 be a root of y = 4x2 - 14x + q = 0. Then y is equal to

Question

Let x = 2 be a root of y = 4x2 - 14x + q = 0. Then y is equal to (A) (x - 2) (4x - 6) (B) (x - 2) (4x + 6) (C) (x - 2) (-4x - 6) (D) (x - 2) (-4x + 6)

Tardigrade Admin · Accepted Answer

We have y=4 x2-14 x+q=0 Since, x=2 is the root ∴ 4(2)2-14(2)+q=0 ⇒ 16-28+q=0 ⇒ q=12 ∴ y=4 x2-14 x+12 =4 x-8 x-6 x+12 =4 x(x-2)-6(x-2) =(x-2)(4 x-6)

Q. Let $x = 2$ be a root of $y = 4 x^{2} - 14 x + q = 0$ . Then $y$ is equal to

(x - 2) (4x - 6)

(x - 2) (4x + 6)

(x - 2) (-4x - 6)

(x - 2) (-4x + 6)

(x - 2) (4x + 3)

We have
$y = 4 x^{2} - 14 x + q = 0$
Since, $x = 2$ is the root
$∴ 4 (2)^{2} - 14 (2) + q = 0$
$\Rightarrow 16 - 28 + q = 0$
$\Rightarrow q = 12$
$∴ y = 4 x^{2} - 14 x + 12$
$= 4 x - 8 x - 6 x + 12$
$= 4 x (x - 2) - 6 (x - 2)$
$= (x - 2) (4 x - 6)$

Q. Let x=2 be a root of y=4x2−14x+q=0. Then y is equal to