Create a quadratic polynomial whose sum and product of zeros are 1/4 and −1 respectively.

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Recall the sum and product of zeros for the quadratic ax² + bx + c = 0 . Sum of zeros: s = −b/a; Product of zeros: p = c/a; Given: s = 1/4 , p = −1/4; s = −b/a = 1/4; p = c/a = −1/4; Step 2: Choose a = 4 to obtain integer coefficients. Substitute a = 4 into sum formula: −b/4 = 1/4 Multiply both sides by −4: b = −1; Step 3: Substitute a = 4 into product formula: c/4 = −1/4 Multiply both sides by 4: c = −1 Step 4: Form the quadratic polynomial. 4x² + (−1)x + (−1) = 4x² − x − 1 Step 5: Verify sum and product. Sum: −b/a = −(−1)/(4) = 1/4; Product: c/a = (−1)/(4) = −1/4 4x² − x − 1

Create a quadratic polynomial whose sum and product of zeros are 1/4 and -1 respectively.

Answer

Step-by-step solution

Recall the sum and product of zeros for the quadratic $ax^2 + bx + c = 0$ .

Choose $a = 4$ to obtain integer coefficients.

Substitute $a = 4$ into product formula

Form the quadratic polynomial.

Verify sum and product.

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