Question

If alpha,beta are the zeroes of x²-3x+p. What is the value of p, if 2alpha + 3beta = 15​

Answer 1

Answer:

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Step-by-step explanation:

Given that α & β are zero of polynomial

f(x)=x2−3x−2

therefore α+β=3

αβ=−2

Now, the zero of the required quadratic polynomial are,

2α+β1 & 2β+α1

Sum of the roots-

2α+β1+2β+α1=(2α+β)(2β+α)2β+α+2α+β=4αβ+2α2+2β2+αβ3(α+β)

=4×(−2)+2[(α+β)2−2αβ]+(−2)3×3

=−10+2[9+2×2]9

=−10+269

=169

Products of roots:-

2α+β1×2β+α1=