Advertisements
Advertisements
प्रश्न
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
उत्तर
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
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
48x² – 13x -1 = 0
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
