If the expression x 2+ Kxy +7 x +4 y +10 resolved into two linear factors then the sum of all integral values of K is equal to

Question

If the expression x 2+ Kxy +7 x +4 y +10 resolved into two linear factors then the sum of all integral values of K is equal to (A) 2 (B) 5 (C) 7 (D) 14

Tardigrade Admin · Accepted Answer

a=1, b=0, c=10, f=2, g=(7/2), h=(K/2) a b c+2 f g h-a2-b2-c2=0 ⇒ 2 × 2 × (7/2) × (K/2)-4-10 × (K2/4)=0 ⇒ 5 K2-14 K+8=0 ⇒ (K-2)(5 K-4)=0 K=2

Q. If the expression $x^{2} + K x y + 7 x + 4 y + 10$ resolved into two linear factors then the sum of all integral values of $K$ is equal to

2

5

7

14

$a = 1, b = 0, c = 10, f = 2, g = \frac{7}{2}, h = \frac{K}{2}$
$ab c + 2 f g h - a^{2} - b^{2} - c^{2} = 0$
$\Rightarrow 2 \times 2 \times \frac{7}{2} \times \frac{K}{2} - 4 - 10 \times \frac{K ^{2}}{4} = 0$
$\Rightarrow 5 K^{2} - 14 K + 8 = 0$
$\Rightarrow (K - 2) (5 K - 4) = 0$
$K = 2$

Q. If the expression x2+Kxy+7x+4y+10 resolved into two linear factors then the sum of all integral values of K is equal to

2

5

7

14

a=1,b=0,c=10,f=2,g=27​,h=2K​ abc+2fgh−a2−b2−c2=0 ⇒2×2×27​×2K​−4−10×4K2​=0 ⇒5K2−14K+8=0 ⇒(K−2)(5K−4)=0 K=2

Q. If the expression $x^{2} + K x y + 7 x + 4 y + 10$ resolved into two linear factors then the sum of all integral values of $K$ is equal to

$a = 1, b = 0, c = 10, f = 2, g = \frac{7}{2}, h = \frac{K}{2}$
$ab c + 2 f g h - a^{2} - b^{2} - c^{2} = 0$
$\Rightarrow 2 \times 2 \times \frac{7}{2} \times \frac{K}{2} - 4 - 10 \times \frac{K ^{2}}{4} = 0$
$\Rightarrow 5 K^{2} - 14 K + 8 = 0$
$\Rightarrow (K - 2) (5 K - 4) = 0$
$K = 2$