find the value of p such that the quadratic equation x^2-(p+6)x+2(2p-1) =0 has sum of the roots as half of their product

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equation is x² - (p + 6)x + 2(2p - 1) = 0.

Sum of the roots is half of their product

the value of p

Let ,

And,

Sum of the roots is half of their product.

We know that,

Sum of the zeroes = - b/a

→ sum of the zeroes = - [ - (p + 6) ] / 1

→ sum of the zeroes = p + 6

Product of the zeroes = c/a

→ Product of the zeroes = 2(2p - 1)

Hence,

→ p + 6 = 1/2 * 2(2p - 1)

→ p + 6 = 2p - 1

→ 6 + 1 = 2p - p

→ 7 = p

Therefore, the value of p is 7.

I hope it will help you.

Regards.