Advertisements
Advertisements
Question
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’
Advertisements
Solution
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
RELATED QUESTIONS
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
The quadratic equation whose one rational root is `3 + sqrt2` is
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 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 ______.
Which of the following equations has imaginary roots?
