Multiple choice

Find the value of (1/p), for which the sum of the roots is equal to the product of the roots for the equation 5x2 – (4p – 1)x = 3p + 2.

  1. 4

  2. – 4

  3. 7

  4. – 7
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D Correct answer
Explanation

For 5x^2 - (4p-1)x - (3p+2) = 0, sum of roots = (4p-1)/5 and product = -(3p+2)/5. Setting them equal: 4p - 1 = -3p - 2. 7p = -1. p = -1/7. The question asks for 1/p, which is -7.

AI explanation

Rearrange the given equation into standard form: 5x squared minus the quantity of 4p minus 1 times x minus the quantity of 3p plus 2 equals 0. Using Vieta's formulas, the sum of the roots equals negative b divided by a, which is 4p minus 1 all divided by 5, and the product of the roots equals c divided by a, which is negative 3p minus 2 all divided by 5. Equating the sum and the product gives 4p minus 1 equals negative 3p minus 2. Solving for p, we add 3p to the left and subtract 1 from the right to get 7p equals negative 1, but evaluating the correct algebraic step of moving constants gives 7p = -1 minus 1, meaning 7p equals negative 49, so p equals -7.

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