Advertisements
Advertisements
Question
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Advertisements
Solution
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
a = `sqrt 3` ; b = 10 ; c = `-8/sqrt 3`
D = b2 - 4ac
= `(10)^2 - 4 (sqrt 3) (-8 sqrt 3)`
= 100 + 96
= 196
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(- 10 +- sqrt 196)/(2 sqrt 3)`
x = `(-10 + 14)/(2 sqrt 3)` , x = `(-10 - 14)/(2 sqrt 3)`
x = `4/(2 sqrt 3)` , x = `24/(2 sqrt 3)`
x = `2/sqrt 3` , x = `-12/ sqrt 3`
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 value of p for which the quadratic equation (p + 1)x2 − 6(p + 1)x + 3(p + 9) = 0, p ≠ − 1 has equal roots. Hence find the roots of the equation.
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Solve the following quadratic equation using formula method only
`3"x"^2 + 2 sqrt 5x - 5 = 0 `
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
