Advertisements
Advertisements
प्रश्न
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Advertisements
उत्तर
The given quadric equation is kx2 + 6x + 1 = 0, and roots are real and distinct.
Then find the value of k.
Here,
a = k, b = 6 and c = 1
As we know that D = b2 - 4ac
Putting the value of a = k, b = 6 and c = 1
D = (6)2 - 4 x (k) x (1)
= 36 - 4k
The given equation will have real and distinct roots, if D > 0
36 - 4k > 0
Now factorizing of the above equation
36 - 4k > 0
4k < 36
k < 36/4
k < 9
Now according to question, the value of k less than 9
Therefore, the value of k < 9.
APPEARS IN
संबंधित प्रश्न
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Solve the following quadratic equation using formula method only
5x2 - 19x + 17 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x2 + 2(k – 4) x + 4 = 0
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real 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:
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
