If the equations x3+10 x2+a x+b=0 and x3+4 x2+a x+c=0(a, b, c ∈ R) have two roots in common then

Question

If the equations x3+10 x2+a x+b=0 and x3+4 x2+a x+c=0(a, b, c ∈ R) have two roots in common then (A) product of uncommon roots equals -40 . (B) 4 a=c. (C) 10 a - b =0. (D) sum of common roots equals 0 .

Tardigrade Admin · Accepted Answer

Correct answer is (b) 4 a=c.Correct answer is (c) 10 a - b =0.Correct answer is (d) sum of common roots equals 0 .

Q. If the equations $x^{3} + 10 x^{2} + a x + b = 0$ and $x^{3} + 4 x^{2} + a x + c = 0 (a, b, c \in R)$ have two roots in common then

product of uncommon roots equals -40 .

$4 a = c$ .

$10 a - b = 0$ .

sum of common roots equals 0 .

Correct answer is (b) $4 a = c$ . Correct answer is (c) $10 a - b = 0$ . Correct answer is (d) sum of common roots equals 0 .

Q. If the equations x3+10x2+ax+b=0 and x3+4x2+ax+c=0(a,b,c∈R) have two roots in common then

product of uncommon roots equals -40 .

4a=c.

10a−b=0.

sum of common roots equals 0 .

Correct answer is (b) 4a=c. Correct answer is (c) 10a−b=0. Correct answer is (d) sum of common roots equals 0 .

Q. If the equations $x^{3} + 10 x^{2} + a x + b = 0$ and $x^{3} + 4 x^{2} + a x + c = 0 (a, b, c \in R)$ have two roots in common then

$4 a = c$ .

$10 a - b = 0$ .

Correct answer is (b) $4 a = c$ . Correct answer is (c) $10 a - b = 0$ . Correct answer is (d) sum of common roots equals 0 .