Question

please ans it urgent both questions

Answer 1

Hey there !!!!!

If a quadratic polynomial p(x)=ax²+bx+c has α and β as the zeroes of the polynomial 
then     α+β =-b/a     αβ=c/a

              
Now, p(x) = 2x²+5x+1 and α,β are zeroes of p(x)

α+β+αβ = -b/a+ c/a =(c-b)/a

 Here a = 2  b=5 c=1

α+β+αβ = (1-5)/2 =-4/2 =-2

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2)If a,b,r are zeroes of p(x) = x³-6x²+11x-6 

  Now if a cubic polynomial of the form Ax³+Bx²+Cx+D=0 which has roots as α,β,γ

Then sum of the roots α+β+γ =-B/A

Sum and product = αβ+αγ+βγ= C/A

Product of roots =αβγ = -D/A

In p(x) = x³-6x²+11x-6 

A=1 B= -6 C=11 D=-6

Sum of roots

     a+b+r=-B/A

     a+b+r =-(-6)/1

      a+b+r =6---- Equation 1
sum and product of roots = ab+br+ar=C/A=11--- Equation 2

Squaring equation 1 on both sides

   (a+b+r)² = 6²

   a²+b²+r²+2(ab+br+ar)=6²

Now from equation 2

      a²+b²+r²+2(11)=6²

    a²+b²+r²= 36-22

   a²+b²+r²=14

Hope this helped you............