Advertisements
Advertisements
प्रश्न
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
उत्तर
The given quadratic equation is 3x2 − 2kx + 12 = 0
On comparing it with the general quadratic equation ax2 + b x + c = 0, we obtain
a = 3, b = −2k and c = 12
Discriminant, ‘D’ of the given quadratic equation is given by
D = b2 − 4ac
= (− 2k)2 − 4 × 3 × 12
= 4k2 − 144
For equal roots of the given quadratic equations, Discriminant will be equal to 0.
i.e., D = 0
`rArr 4k^2-144=0`
`rArr4(k^2-36)=0`
`rArrk^2=36`
`rArrk=+-6`
Thus, the values of k for which the quadratic equation 3x2 − 2kx + 12 = 0 will have equal roots are 6 and −6.
APPEARS IN
संबंधित प्रश्न
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Discuss the nature of the roots of the following quadratic equations : x2 – 4x – 1 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
