Advertisements
Advertisements
Question
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
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
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Solve x2/3 + x1/3 - 2 = 0.
In each of the following determine the; value of k for which the given value is a solution of the equation:
x2 + 2ax - k = 0; x = - a.
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4 , b = ______ , c = 3
b2 – 4ac = (– 5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
