Given, 3x2 + 2x + k = 0 It’s of the form of ax2 + bx + c = 0 Where, a =3, b = 2, c = k For the given quadratic equation to have real roots D = b2 – 4ac ≥ 0 D = (2) 2 – 4(3)(k) ≥ 0 ⇒ 4 – 12k ≥ 0 ⇒ 4 ≥ 12k ⇒ k ≤ 1/3 The value of k should not exceed 1/3 to have real roots. Check out the video given below to know more about quadratic equations  Further Reading
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 |
12. find the value of k for which the quadratic equation 3x ^ 2 + 2x + k = 0 has two real roots.
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