Advertisements
Advertisements
Question
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Solution
`2x + 5 sqrt 3x +6= 0 `
a = 2 ; b = `5 sqrt 3` ; c = 6
D = b2 - 4ac
D = `(5 sqrt 3)^2 - 4(2)(6)`
= 75 - 48
= 27
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(-(5 sqrt 3) +- 3 sqrt 3)/4`
x = `(-(5 sqrt 3) + 3 sqrt 3)/4` , x = `(-(5 sqrt 3) - 3 sqrt 3)/4`
x = `(-2 sqrt 3)/4` , x = `(- 8 sqrt 3)/4`
x = `- sqrt 3/2` , x = `- 2 sqrt 3`
APPEARS IN
RELATED QUESTIONS
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
