Question

solve for y. y^{2}-10y + 21 = 0 if there is more than one solution, separate them with commas. if there is no solution, click on
o solution\.

Explanation:

Step1: Identify coefficients for quadratic formula

For the quadratic equation $y^{2}-10y + 21=0$, we have $a = 1$, $b=-10$, $c = 21$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(-10)^{2}-4\times1\times21=100 - 84=16$.

Step3: Use the quadratic formula

The quadratic formula is $y=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substitute $a = 1$, $b=-10$, $\Delta = 16$: $y=\frac{10\pm\sqrt{16}}{2\times1}=\frac{10\pm4}{2}$.

Step4: Find the two solutions

For the plus - case: $y=\frac{10 + 4}{2}=\frac{14}{2}=7$. For the minus - case: $y=\frac{10-4}{2}=\frac{6}{2}=3$.

Answer:

$3,7$