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ax^2+bx+c=0 has real roots a1x^2+b1x+c1=0 has real roots then the roots of (a+a1)x^2+(b+b1)x+c+c1=0

ax^2+bx+c=0 has real roots a1x^2+b1x+c1=0 has real roots then the roots of (a+a1)x^2+(b+b1)x+c+c1=0

Grade:11

1 Answers

Y RAJYALAKSHMI
45 Points
9 years ago
Ans:  may be real or non real.roots
 
Case 1:   let ax^2+bx+c=0 be x^2 + 2x + 1 = 0  & a1x^2+b1x+c1=0 be  x^2 – 2x + 1 = 0 
then (a+a1)x^2+(b+b1)x+c+c1=0 will be x^2 + 2 = 0 which has non real roots.
 
Case 2:  let ax^2+bx+c=0 be x^2 + 2x + 1 = 0  & a1x^2+b1x+c1=0 be  2x^2 + 9x + 4 = 0 
then (a+a1)x^2+(b+b1)x+c+c1=0 will be 3x^2 + 11x + 5 = 0 which has real roots.
 
 

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