Exams › JEE Main › Maths

The polynomial z⁵ - 32 factors over the reals as (z - 2)(z² - p z + 4)(z² - q z + 4). Find p² + 2p.

1. 4
2. 1 + sqrt(5)
3. (sqrt(5) - 1)² + 2(sqrt(5) - 1) over 4
4. 5

Correct answer: 4

Solution

p and q are 4cos72deg and 4cos144deg. Using cos72 + cos144 = -1/2 and the value of p, p² + 2p evaluates to 4.

Related JEE Main Maths questions

• Given z1 = √3 + i√3 and z2 = √3 + i, determine the quadrant in which the complex number z1/z2 lies.
• For the quadratic equation 2(1+i)x² − 4(2−i)x − (5+3i) = 0, the root with the larger absolute value is
• Find the value of ((cosθ+isinθ)⁴)/((cosθ-isinθ)³).
• How many complex numbers z satisfy the equation z³ + (3|z|²)/(z) = 0, given that |z| = √(3)?
• Let z = x + iy be a variable complex number. If arg((z - 1)/(z + 1)) = π/4, then which relation is satisfied?
• For positive values of a, b and c, consider the quadratic equation ax² + bx + c = 0. What can be said about its two roots?

⚔️ Practice JEE Main Maths free + battle 1v1 →