If the quadratic equation x2 + 4x + a = 0 has real and equal roots, then
Question
If the quadratic equation x2 + 4x + a = 0 has real and equal roots, then
Solution
To find the condition for the quadratic equation x^2 + 4x + a = 0 to have real and equal roots, we can use the discriminant. The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, the coefficients are a = 1, b = 4, and c = a. Substituting these values into the discriminant formula, we get (4)^2 - 4(1)(a).
For the equation to have real and equal roots, the discriminant must be equal to zero. So, we set the discriminant equal to zero and solve for a:
(4)^2 - 4(1)(a) = 0 16 - 4a = 0 -4a = -16 a = 4
Therefore, the value of a that makes the quadratic equation x^2 + 4x + a = 0 have real and equal roots is a = 4.
Similar Questions
A quadratic equation ax2 + bx + c = 0, such that a + b + c = 0, has equal roots. Which of the following statements must be true?b = 2aa = 4ca2 + b2 = c2a = c
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is:(a) No real roots (b) 2 equal real roots(c) 2 distinct real roots (d) More than 2 real roots
Find the nature of the roots of the quadratic equation 2x2-3x=0
The quadratic equation x kx2 2 02 + + = has equal roots, if the value of k is:(a) – 4 (b) 2(c) ± 4 (d) 4
Find the quadratic equation whose roots are twice the roots of the quadratic equation 4x2 – 16x + 15 = 0.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.