Advertisements
Advertisements
प्रश्न
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
Advertisements
उत्तर
px2 – 4x + 3 = 0
Here a = p, b = −4 and c = 3
Given equation has equal roots
Then D = 0
`=>` b2 – 4ac = 0
`=>` [–4]2 – 4(p)(3) = 0
`=>` 16 – 12p = 0
`=>` –12p = –16
`=> p = (-16)/(-12) = 4/3`
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 + 3 = 0
If the roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then prove that 2b = a + c.
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.
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
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`
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
