Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
उत्तर
The given equation is 2x2 + kx + 3 = 0
The given equation is in the form of
ax2 + bx + c = 0
where a = 2, b = k and c = 3
Therefore, the discriminant
D = b2 - 4ac
= k2 - 4 x (2) x (3)
= k2 - 24
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ k2 - 24 = 0
⇒ k2 = 24
`rArrk=sqrt24`
`rArrk=+-sqrt(4xx6)`
`rArrk=+-2sqrt6`
Hence, the value of `k=+-2sqrt6`
APPEARS IN
संबंधित प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
Find the value(s) of p for which the quadratic equation (2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
