Advertisements
Advertisements
प्रश्न
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
Advertisements
उत्तर
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`
संबंधित प्रश्न
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 – 6x + 3 = 0
Find the value of the discriminant in the following quadratic equation:
2x2 - 3x + 1 = O
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Solve for x: (x2 - 5x)2 - 7(x2 - 5x) + 6 = 0; x ∈ R.
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
(x2 + 1)2 – x2 = 0 has:
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
