Advertisements
Advertisements
Question
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Advertisements
Solution
The given quadric equation is 4x2 − 12x − 9 = 0
Here, a = 4, b = -12 and, c = -9
As we know that `D = b^2 - 4ac`
Putting the value of
`a = 4, b = -12 and c = -9`
`(-12)^2 - 4 xx 4 xx -9`
= 144 + 144
= 288
Since, D ≥ 0
Therefore, root of the given equation are real and distinct .
APPEARS IN
RELATED QUESTIONS
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.
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.
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 2(k + 1)x + (k + 4) = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b2 = ac.
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
`10x -(1)/x` = 3
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
