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Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Concept: Nature of Roots of a Quadratic Equation
Find that value of p for which the quadratic equation (p + 1)x2 – 6(p + 1)x + 3(p + 9) = 0, p ≠ –1 has equal roots. Hence, find the roots of the equation.
Concept: Nature of Roots of a Quadratic Equation
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Concept: Nature of Roots of a Quadratic Equation
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
Concept: Nature of Roots of a Quadratic Equation
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
Concept: Nature of Roots of a Quadratic Equation
If ad ≠ bc, then prove that the equation (a2 + b2)x2 + 2(ac + bd)x + (c2 + d2) = 0 has no real roots.
Concept: Nature of Roots of a Quadratic Equation
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Concept: Nature of Roots of a Quadratic Equation
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Concept: Nature of Roots of a Quadratic Equation
If x = −2 is a root of the equation 3x2 + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x2 + k(4x + k − 1) + p = 0 are equal.
Concept: Nature of Roots of a Quadratic Equation
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
Concept: Nature of Roots of a Quadratic Equation
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Concept: Nature of Roots of a Quadratic Equation
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Concept: Nature of Roots of a Quadratic Equation
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
Concept: Nature of Roots of a Quadratic Equation
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
Concept: Nature of Roots of a Quadratic Equation
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
Concept: Nature of Roots of a Quadratic Equation
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
Concept: Nature of Roots of a Quadratic Equation
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Concept: Nature of Roots of a Quadratic Equation
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
Concept: Nature of Roots of a Quadratic Equation
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
Concept: Nature of Roots of a Quadratic Equation
Solve for x: 9x2 – 6px + (p2 – q2) = 0
Concept: Nature of Roots of a Quadratic Equation
