Roots of polynomials

The roots of the equation 20x³ – 16x² – 4x + 7 = 0 are α, β and γ

Find the value of αβ + βγ + γα

Circle your answer.

The cubic equation x³ + 5x² – 4x + 2 = 0

has roots α, β and γ

Find a cubic equation, with integer coefficients, whose roots are 3α, 3β and 3γ

The quadratic equation z² 5z 8 0 has roots and

Write down the value of and the value of

Without finding the value of or the value of , show that ^{4 4} 47

Find a quadratic equation, with integer coefficients, which has roots ³

The equation

has roots , and

Find a cubic equation with roots

The quadratic equation ax² bx c 0 (a, b, c ) has real roots and .

One of the four statements below is incorrect.

Which statement is incorrect ?

Tick () one box.

The three roots of the equation

where k is a constant, form an arithmetic sequence.

Find the roots of the equation.

The equation z³ kz² 9 0 has roots , and .

The equation 9z³ 40z² rz s 0 has roots , and .

Show that

Without calculating the values of , and , find the value of s.

Show working to justify your answer.