Question

if alpha and beta are zeroes of equations p(x) = 3x^2+ 11x + a form a quadratic equations whose zeroes are 3a and 3b​

Answer 1

Eq. = 3x² + 11x + a

Sum of zeroes = - (coefficient of x) / (coefficient of x²)

==> α + β = - 11/3

Multiply both sides by 3

==> 3α + 3β = -11 ...(1)

Also,

Product of zeroes = ( constant term ) / ( coefficient of x² )

==> αβ = a / 3

Multiply each equation by 9

==> 3α × 3β = 3a ...(1)

We know,

Quad. Equation = x² - ( sum of zeroes )x + ( product of zeroes )

==> x² - ( - 11)x + 3a

==> x² + 11x + 3a

Hence, the required quadratic equation is

☛ x² + 11x + 3a