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
Solve the equation by using the formula method. 3y2 +7y + 4 = 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 value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
Every quadratic equation has at least two roots.
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.
