The expression `y = ax^2+ bx + c` has always the same sign as of a if `(A) 4ac < b^2 (B) 4ac > b^2 (C) 4ac= b2 (D) ac < b^2`

If alpha, beta are the roots of the equation ax ^(2) + bx + c =0, then the value of (1)/( a alpha + b) + (1)/( a beta + b) equals to : a) (ac)/(b) b) 1 c) (ab)/(c) d) (b)/(ac)

If ax^(2)+bx+c is a perfect square,then prove that b backslash b^(2)=4ac

If the roots of ax^(2)+bx+c=0 are real and equal then ………….. A) b^(2)-4ac lt 0 B) b^(2)-4ac=0 C) b^(2)-4ac gt 0 D)cannot say

Let alpha and beta be the roots of the equationa ax^2 + bx + c = 0 and alpha + gamma and beta + gamma be the roots of Ax^2 + Bx + C = 0. Then prove that A^2(b^2 - 4ac) = a^2(B^2 - 4AC).

If r is the ratio of the roots of the equation ax^(2)+bx+c=0, then r is the root of the equation.(A) acx^(2)+(2ac-b^(2))x+ac=0 (C) acx^(2)+(2ac-b^(2))x-ac=0 (B) acx^(2)-(2ac-b^(2))x+ac=0(D)acx^(2)-(2ac-b^(2))x-ac=0

If the equation ax^2+bx+c=0(a>0) has two roots α and β such that α 2 , then: a) b^2-4ac>0 b) c 0 d) 4a+2|b|+c <0

Statement -1 : The quadratic equation ax^(2)+bx+c=0 has real roots if (a+c)^(2) gt b^(2) , AA , a,b,c in R . and Statement -2 : The quadratic equation ax^(2) +bx+c=0 has real roots if b^(2) -4ac ge 0

If sinthetaand costheta are the roots of the equation ax^2+bx+c=0 , then (A) (a-c)^2=b^2+c^2 (B) (a+c)^2=b^2-c^2 (C) a^2=b^2-2ac (D) a^2+b^2-2ac=0