Advertisements
Advertisements
प्रश्न
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’
Advertisements
उत्तर
3y2 + ky + 12 = 0
Comparing the above equation with
ax2 + by + c = 0, we get
a = 3, b = k, c = 12
∆ = b2 – 4ac
= (k)2 – 4 × 3 × 12
= k2 – 144
= k2 – (12)2
∆ = (k + 12)(k – 12) ......[∵ a2 – b2 = (a + b)(a − b)]
Since the roots are real and equal,
∆ = 0
∴ (k + 12)(k – 12) = 0
∴ k + 12 = 0 or k – 12 = 0
∴ k = – 12 or k = 12
संबंधित प्रश्न
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(5 + 2k)x + 3(7 + 10k) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
5x2 - 4x + 2 + k(4x2 - 2x - 1) = 0
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.
ax2 + (4a2 - 3b)x - 12 ab = 0
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
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the values of p for which the equation 3x2 – px + 5 = 0 has real roots.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
Which of the following equations has 2 as a root?
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
Every quadratic equation has exactly one root.
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
