Advertisements
Advertisements
Question
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
Advertisements
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 = `(-(-3sqrt(5)) +- sqrt((-3sqrt(5))^2 - 4(1)(10)))/(2(1))`
= `(3sqrt(5) +- sqrt(5))/2`
= `2sqrt(5), sqrt(5)`
APPEARS IN
RELATED QUESTIONS
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b2 = ac.
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
(3x - 5)(2x + 7) = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
kx2 + 2x + 3k = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
Choose the correct answer from the given four options :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
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`
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least is ______.
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
