Question

which are the roots of the quadratic function f(b) = b2 – 75? check all that apply. b = 5 square root of 3 b = -5 square root of 3 b = 3 square root of 5 b = -3 square root of 5 b = 25 square root of 3 b = -25 square root of 3

Answer 1

The answers are b = 5 square root of 3; b = -5 square root of 3. f(b) = b^2 – 75. If f(b) = 0, then b^2 – 75 ) 0. b^2 = 75. b = √75. b = √(25 * 3). b = √25 * √3. b = √(5^2) * √3. Since √x is either -x or x, then √25 = √(5^2) is either -5 or 5. Therefore. b = -5√3 or b = 5√3.

Answer 2

Answer:

$b=5\sqrt{3}$ and $b=-5\sqrt{3}$ are the roots of given quadratic equation.

Step-by-step explanation:

Given quadratic equation is $f(b)=b^2-75$

We have to check all the given options.

If the value of f(b) gives 0 when put the value of b in above equation then only that b value is the root of quadratic equation.

$b=5\sqrt{3}: (5\sqrt{3})^{2}-75=75-75=0$

$b=-5\sqrt{3}: (-5\sqrt{3})^{2}-75=75-75=0$

$b=3\sqrt{5}: (3\sqrt{5})^{2}-75=45-75=30\neq 0$

$b=-3\sqrt{5}: (-3\sqrt{5})^{2}-75=45-75=30\neq 0$

$b=25\sqrt{3}: (25\sqrt{3})^{2}-75=1875-75=1800\neq 0$

$b=-25\sqrt{3}: (-25\sqrt{3})^{2}-75=1875-75=1800\neq 0$

hence, only first two values $b=5\sqrt{3},-5\sqrt{3}$ gives the value of f(b)=0 .

⇒ $b=5\sqrt{3}$ and $b=-5\sqrt{3}$ are the roots of given quadratic equation.