Advertisements
Advertisements
Question
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
Advertisements
Solution
Given equation is `x^2 + 5sqrt(5)x - 70` = 0
On company with ax2 + bx + c = 0, we get
a = 1, b = `5sqrt(5)` and c = – 70
∴ Discriminant, D = b2 – 4ac
= `(5sqrt(5))^2 - 4(1)(-70)`
= 125 + 280
= 405 > 0
Therefore, the equation `x^2 + 5sqrt(5)x - 70` = 0 has two distinct real roots.
Roots, `x = (-b +- sqrt(D))/(2a)`
= `(-5sqrt(5) +- sqrt(405))/(2(1))`
= `(-5sqrt(5) +- 9sqrt(5))/2`
= `(-5sqrt(5) + 9 sqrt(5))/2, (-5sqrt(5) - 9sqrt(5))/2`
= `(4sqrt(5))/2, - (14 sqrt(5))/2`
= `2sqrt(5), -7sqrt(5)`
APPEARS IN
RELATED QUESTIONS
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
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
`(2)/x^2 - (5)/x + 2` = 0
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
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 the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
The roots of the quadratic equation `"x" + 1/"x" = 3`, x ≠ 0 are:
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
