Advertisements
Advertisements
Question
Find the value of ๐ so that the quadratic equation ๐๐ฅ(5๐ฅ − 6) = 0 has two equal roots.
Advertisements
Solution
5mx2 – 6mx + 9 = 0
b2 – 4ac = 0 ⇒ (– 6m)2 – 4(5m)(9) = 0
⇒ 36m(m – 5) = 0
⇒ m = 0, 5 ; rejecting m = 0, we get m = 5
APPEARS IN
RELATED QUESTIONS
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(k + 1)x + (k + 4) = 0
Find the values of k for which the roots are real and equal in the following quadratic equation:
k2x2 – 2(2k – 1)x + 4 = 0
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
What expression gives the discriminant of a quadratic equation \( ax^{2} + bx + c = 0 \)?
When the discriminant satisfies \( D > 0 \), what is the nature of the roots of the quadratic equation?
