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
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
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.
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.
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x− 2(p − q) = 0 are real and unequal.
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Choose the correct answer from the given four options :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
The roots of quadratic equation 5x2 – 4x + 5 = 0 are:
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
Equation 2x2 – 3x + 1 = 0 has ______.
