Advertisements
Advertisements
Question
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Advertisements
Solution
9a2b2x2 - 48abc + 64c2d2 = 0
Here, D = b2 - 4ac
⇒ (-48abcd)2 - 4 x 9a2b2 x 64c2d2
2304a2b2c2d2 - 2304a2b2c2d2 = 0
D = 0
Roots are real and equal.
RELATED QUESTIONS
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
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 ?
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Which of the following equations has two distinct real roots?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
Every quadratic equation has at least two roots.
