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For which values of p will the equation x(4x+3)=-p have real roots

User TLama
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Answer:

For values of p less than or equal to 9/16, the equation x(4x+3)=-p will have real roots.

Explanation:

The given equation is x(4x+3)=-p.

To find the values of p for which the equation has real roots, we can use the discriminant of the quadratic equation.

The quadratic equation formed by the given equation is 4x^2 + 3x + p = 0.

The discriminant of this quadratic equation is:

D = b^2 - 4ac

= 3^2 - 4(4)(p)

= 9 - 16p

For the equation to have real roots, the discriminant must be non-negative, i.e., D ≥ 0.

Therefore, we have:

9 - 16p ≥ 0

Solving for p, we get:

p ≤ 9/16

Hence, for values of p less than or equal to 9/16, the equation x(4x+3)=-p will have real roots. For values of p greater than 9/16, the equation will have complex roots.

User Jayrox
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