Advertisements
Advertisements
Question
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Solution
The quadratic formula for finding the roots of quadratic equation
ax2 + bx + c = 0, a ≠ 0 is given by,
x = `(-b +- sqrt(b^2 - 4ac))/(2a)`
∴ x = `(-(-sqrt(11)) +- sqrt((-sqrt(11))^2 - 4(1/2)(1)))/(2(1/2))`
= `(sqrt(11) +- sqrt(9))/1`
= `sqrt(11) +- 3`
= `3 + sqrt(11), -3 + sqrt(11)`
APPEARS IN
RELATED QUESTIONS
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
Find the values of k for which the roots are real and equal in each of the following equation:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
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)`
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Find whether the following equation have real roots. If real roots exist, find them.
`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
