Question

If a and b are the roots of x + 7x + 10 = 0 find the value of a^4 + b^4​

Answer 1

Answer:

Let α be the common root.

∴α

2

−7α+10=0 ...(1)

and ∴α

2

−10α+16=0 ...(2)

Subtracting (2) from (1)

∴(α

2

−7α+10)−(α

2

−10α+16)=0−0

∴3α−6=0

∴α=2

Answer 2

$x^{2}$+7x+10=0

$x^{2}$+2x+5x+10=0

x(x+2)+5(x+2)=0

(x+5)(x+2)=0

a= -5 and b= -2

$a^{4} +b^{4} =(-5)^{4} +(-2)^{4}$ $=625+16=641$