Find the zeros of the quadratic polynomial $9x^2-5$.
- $\cfrac { { 5 } }{ 9 } , -\cfrac { 5 }{ 9 } $
- $\cfrac { { 5 } }{ 3 } , -\cfrac { 5 }{ 3 } $
- $\cfrac { \sqrt { 5 } }{ 3 } , -\cfrac { \sqrt { 5 } }{ 3 } $
- $\cfrac { \sqrt { 3 } }{ 5 } , -\cfrac { \sqrt { 3 } }{ 5 } $
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C
Correct answer
Explanation
Set 9x^2 - 5 = 0. Then x^2 = 5/9, so x = +/- sqrt(5)/3.
AI explanation
To find the zeros of the polynomial 9x^2 - 5, we set the expression equal to zero, resulting in 9x^2 - 5 = 0. Solving for x^2, we add 5 to the right side to get 9x^2 = 5, and then divide by 9 to isolate x^2, giving x^2 = 5/9. Taking the square root of both sides of the equation yields x = sqrt(5/9). Because the square root of a fraction is the fraction of the square roots, the final values for the zeros are sqrt(5)/3 and -sqrt(5)/3.