The equation `4ax^2 + 3bx + 2c = 0` where a, b, c are real and a+b+c = 0 has

If the equation ax^2 + bx + c = 0 ( a gt 0) has two roots alpha and beta such that alpha 2 , then

Consider a quadratic equation ax^2 + bx + c = 0 having roots alpha, beta . If 4a + 2b + c > 0,a-b+c 0 then |[alpha] + [beta]| can be {where [] is greatest integer}

Let a, b, c in R and alpha, beta are the real roots of the equation ax​2 + bx + c = 0 and if a + b + c > 0, a – b + c >0 and c < 0 then [alpha] + [beta] is equal to (where [.] denotes the greatest integer function.)

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

If sin alpha, cos alpha are the roots of the equation ax^2 + bx + c = 0 (c ne 0) , then prove that (a+c)^2 = b^2 + c^2 .

If a, b and c are in geometric progression and the roots of the equation ax^(2) + 2bx + c = 0 are alpha and beta and those of cx^(2) + 2bx + a = 0 are gamma and delta

If ax^2 + bx + c = 0, a, b, c in R has no real zeros, and if a + b + c + lt 0, then

If cos A, cosB and cosC are the roots of the cubic x^3 + ax^2 + bx + c = 0 where A, B, C are the anglesof a triangle then find the value of a^2 – 2b– 2c .

Let a, b, c be real numbers with a = 0 and let alpha,beta be the roots of the equation ax^2 + bx + C = 0 . Express the roots of a^3x^2 + abcx + c^3 = 0 in terms of alpha,beta

If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 ( abc ne 0) is equal to the sum of the squares of their reciprocals, the sum of the squares of their reciprocals, then a/c , b/a , c/b are in H.P.