Question

Ifa and b are the roots of the equation x2-2x-15=0, then a+b=​

Answer 1

Answer:

x^2-5x+3x-15=0... x(x-5) +3(x-5)=0.... (x+3) (x-5) =0 x+3=0 x-5=0... x=-3 and x=5 a and b are -3 and 5 respectively.. a+b= (-3) +5 = 2

Answer 2

Answer:

α,β are the roots of x²−2x+4=0

⇒α+β=2,αβ=4

α² +β² =(α+β)² −2αβ

=2² −2(4)

=4−8=−4

Now, α5 +β5 =(α³ +β³)(α² +β²)−α³β² −α²β³

=(α³ +β³ )(α²+β²)−(αβ)² (α+β)

=(−16)(−4)−(4)² (2)

=64−32=32

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