Question

If α and β are zeroes of a quadratic polynomial p(x) = rx^2+4x+4, Find the values of “r” if: – α^2 + β^2 = 24.

Answer 1

Step-by-step explanation:

please refer to Amit goyals book

Answer 2

Answer:

Sum of roots=-b/a

Product of roots=c/a

a²+b²=24

a+b=-4/r

ab=4/r

(a+b)²=a²+b²+2ab

(-4/r)²=24+2(4/r)

16/r²=24+8/r

16/r²-8/r-24=0

16-8r-24r²=0

2-r-3r²=0

3r²+r-2=0

3r²+3r-2r-2=0

3r(r+1)-2(r+1)=0

(3r-2)(r+1)=0

r=2/3, r=-1

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