Find the zeros of the quadratic polynomial $3x^2-12x+9$.

Step-by-step solution

1. Factor out the common factor $3$ from the polynomial.
2. Rewrite the equation as $x^2-4x+3=0$.
3. Factor the quadratic as $(x-1)(x-3)=0$.
4. Set each factor to zero to obtain $x=1$ and $x=3$.

Concept tested: Finding zeros of a quadratic

Published 24 August 2026 · How this solution was prepared and checked

Related questions

• 1 For the cubic polynomial p(x)=x^3-6x^2+11x-6, let its zeros be α,β,γ. Find α^2+β^2+γ^2.
• 2 For the polynomial p(x)=x^4-5x^3+8x^2-4x, find the value of α^2+β^2+γ^2+δ^2, where α,β,γ,δ are its zeros.
• 3 Which of the following linear factors is a factor of the polynomial 2x^3-3x^2-8x+12?
• 4 Find the remainder when the polynomial 5x^4-3x^3+2x-8 is divided by (x+1).
• 5 Without solving, state the sum and product of the roots of the quadratic equation 3x^2-12x+9=0.
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