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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

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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:

[tex]b=5\sqrt{3}[/tex] and [tex]b=-5\sqrt{3}[/tex] are the roots of given quadratic equation.

Step-by-step explanation:

Given quadratic equation is [tex] f(b)=b^2-75[/tex]

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.

[tex]b=5\sqrt{3}: (5\sqrt{3})^{2}-75=75-75=0[/tex]

[tex]b=-5\sqrt{3}: (-5\sqrt{3})^{2}-75=75-75=0[/tex]

[tex]b=3\sqrt{5}: (3\sqrt{5})^{2}-75=45-75=30\neq 0[/tex]

[tex]b=-3\sqrt{5}: (-3\sqrt{5})^{2}-75=45-75=30\neq 0[/tex]

[tex]b=25\sqrt{3}: (25\sqrt{3})^{2}-75=1875-75=1800\neq 0[/tex]

[tex]b=-25\sqrt{3}: (-25\sqrt{3})^{2}-75=1875-75=1800\neq 0[/tex]

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

⇒ [tex]b=5\sqrt{3}[/tex] and [tex]b=-5\sqrt{3}[/tex] are the roots of given quadratic equation.

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