Advertisements
Advertisements
प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Advertisements
उत्तर
The given quadric equation is 3x2 + 2x + k = 0, and roots are real.
Then find the value of k.
Here, a = 3, b = 2 and c = k
As we know that D = b2 - 4ac
Putting the value of a = 3, b = 2 and c = k
= (2)2 - 4 x (3) x (k)
= 4 - 12k
The given equation will have real roots, if D ≥ 0
4 - 12k ≥ 0
12k ≤ 4
k ≤ 4/12
k ≤ 1/3
Therefore, the value of k ≤ 1/3
APPEARS IN
संबंधित प्रश्न
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + 4x + 1 = 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 - 1)x + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
ax2 + (4a2 - 3b)x - 12 ab = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Which of the following equations has 2 as a root?
Choose the correct answer from the given four options :
Which of the following equations has two distinct real roots?
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
Equation (x + 1)2 – x2 = 0 has ____________ real root(s).
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`
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
If 3 is a root of the quadratic equation x2 – px + 3 = 0, then p is equal to ______.
