Advertisements
Advertisements
प्रश्न
Find the values of k for which the given quadratic equation has real and distinct roots:
x2 - kx + 9 = 0
उत्तर
The given quadric equation is x2 - kx + 9 = 0, and roots are real and distinct
Then find the value of k.
Here,
a = 1, b = (-k) and c = 9
As we know that D = b2 - 4ac
Putting the value of a = 1, b = (-k) and c = 9
D = (-k)2 - 4 x (1) x (9)
= k2 - 36
The given equation will have real and distinct roots, if D > 0
k2 - 36 > 0
Now factorizing of the above equation
k2 - 36 > 0
k2 > 36
`k>sqrt36=+-6`
k < -6 Or k > 6
Therefore, the value of k < -6 Or k > 6.
APPEARS IN
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
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.
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots are:
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
