Question Bank
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A two-digit number is such that product of its digits is 18. If 27 is subtracted from number, digits interchange.
If roots of x^2 + ax + b = 0 are tan 30° and tan 15°, find 2 + b - a.
If α, β are roots of x^2 + px + q = 0, find (α-β)^2.
Find the condition for ax^2 + bx + c = 0 to have roots in ratio 3:4.
If x^2 - 5x + 1 = 0, find the value of x^2 + 1/x^2.
If the roots of (b-c)x^2 + (c-a)x + (a-b) = 0 are equal, find the relation between a, b, c.
Find p if roots of 3x^2 + px + 3 = 0 are real and distinct.
If α, β are roots of x^2 - x + 1 = 0, then α^2024 + β^2024 is:
The roots of ax^2 + bx + c = 0 are rational if D is:
The sum of the reciprocals of the roots of 4x^2 + 3x + 7 = 0 is:
If α, β are roots of x^2 - 2x + 4 = 0, find α^3 + β^3.
For what value of k will the equation (k+1)x^2 - 2(k-1)x + 1 = 0 have real roots?
What is the standard form of a quadratic equation?
For the equation x^2 - 5x + 6 = 0, what are the roots?
What is the discriminant (D) of a quadratic equation ax^2 + bx + c = 0?
If the discriminant of a quadratic equation is zero, the roots are:
Find the sum of the roots of the equation 2x^2 - 8x + 5 = 0.