Question

7.      Find the value of k for which the quadratic equation 3x2  +7x + k = 0 has real and equal roots.

Answer 1

Answer:

Step-by-step explanation:

a quadratic equation has equal and real roots when D = 0

also, D (Discriminant) for a quadratic equation = b^2 - 4ac

b^2 - 4ac = 0

(7)^2 - 4(3)(k) = 0

49 - 12k = 0

12k = 49

k =  49/12

hope this helps

Answer 2

The value of k is $\frac{ 49}{12}$

Step-by-step explanation:

Given: A quadratic equation $3x^2 +7x + k = 0$ with real and equal roots

To be found: The value of k

Formula to be used:

Discriminant$, D = b^2 - 4ac$ where a,b, and c are the coefficients of the terms of the quadratic equation

Solution:

• The given equation is $3x^2 +7x + k = 0$

Hence, the three terms are a = 3, b = 7, and c = k

• A quadratic equation that has equal and real roots has the value of D = 0

Thus,

$D = b^2 - 4ac = 0$

Substituting the values

$(7)^2 - 4(3)(k) = 0$

$49 - 12k = 0$

$12k = 49$

$k = \frac{ 49}{12}$

Hence the value of k is $\frac{ 49}{12}$.