The values of k for which the equation 4x2+kx+9=0 has real and equal roots are :
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Step-by-Step Solution
Step 1: Identify coefficients
First, we identify the coefficients a, b, and c from the given quadratic equation 4x2+kx+9=0. Comparing it with the standard form of a quadratic equation, ax2+bx+c=0, we find the values of a, b, and c.
Step 2: Apply condition for real and equal roots
For a quadratic equation to have real and equal roots, its discriminant (D) must be equal to zero. The discriminant is given by the formula D=b2−4ac. We set this expression to zero.
Step 3: Substitute values and solve for k
Now, we substitute the identified values of a=4, b=k, and c=9 into the discriminant equation b2−4ac=0. This gives us an equation in terms of k, which we can then solve.
Step 4: Simplify and find k
We simplify the equation k2−144=0 by adding 144 to both sides. Then, we take the square root of both sides to find the possible values of k. Remember that taking the square root yields both positive and negative solutions.