The parabola y=a x^2+b x+c does not meet the x -axis and passes through the points A(-2,1) and B(2,9) . If range of the abscissa of vertex of parabola is (x₁, x₂ ) , then find the value of |x₁+x₂ |

Step-by-step solution

Given, y=a x^2+b x+c does not intersect the x -axis b^2-4 a c 0 aligned & Also, 1=4 a-2 b+c .....(2) & and 9=4 a+2 b+c .....(3) aligned Now, (3)-(2) 4 b=8 b=2 array ll & 4 a+c=5 .....(4) & c=(5-4 a) array Using, b^2-4 a c 0 aligned & 4-4 a(5-4 a) 0 & 4-20 a+16 a^2 0 & 1-5 a+4 a^2 0 & 4 a^2-5 a+1 0 & 4 a^2-4 a-a+1 0 & 4 a(a-1)-(a-1) 0 & (a-1)(4 a-1) 0 aligned aligned & 1 4 a 1 & 1 2 2 a 2 & 1 b 2 a 4 & -4 - b 2 a -1 & - b 2 a (-4,-1)= ( x ₁, x ₂ ) aligned Hence, |x₁+x₂ |=5