Advertisements
Advertisements
Question
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
Advertisements
Solution
Given quadratic equation is 3x2 – 5x + 2 = 0
D = b2 – 4ac
= (–5)2 – 4(3)(2)
= 25 – 24
= 1
Since D > 0, the roots of the given quadratic equation are real and distinct.
Using quadratic formula, we have
`x = (-b ± sqrt(b^2 - 4ac))/(2a)`
`=> x = (5 ± sqrt((-5)^2 - 4(3)(2)))/(2(3)`
`=> x = (5 ± sqrt(25 - 24))/6`
`=> x = (5 ± 1)/6`
`=> x = (5 + 1)/6` or `x = (5 - 1)/6`
`=> x = 6/6` or `x = 4/6`
`=> x = 1` or `x = 2/3`
APPEARS IN
RELATED QUESTIONS
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.
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 – 3x + 5 = 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:
4x2 + kx + 9 = 0
For what value of k, (4 – k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
If one root of the quadratic equation 2x2 + kx – 6 = 0 is 2, the value of k is:
If (x – a) is one of the factors of the polynomial ax2 + bx + c, then one of the roots of ax2 + bx + c = 0 is:
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
