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3 years ago

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

Mathematics

2 answers:

Stella [2.4K]3 years ago

7 0

Answer:

f(x) = 3x² - 15x + 12

Step-by-step explanation:

Given f(x) has roots x = a and x = b, then

(x - a) and (x - b) are the factors

f(x) is then the product of the factors

f(x) = a(x - a)(x - b) ← where a is a multiplier

Given roots are x = 4 and x = 1, then

(x - 4) and (x - 1) are the factors

With a = 3, then

f(x) = 3(x - 4)(x - 1) ← expand factors using FOIL

= 3(x² - 5x + 4) ← distribute

= 3x² - 15x + 12

Sophie [7]3 years ago

5 0

Answer:

f(x) = 3x^2 - 15x + 12

Step-by-step explanation:

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Read 2 more answers

If m(x) = x^2 + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)?

eduard

(x^2 + 3)(5x + 9)
5x^3 + 9x^2 + 15x + 27

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3 years ago

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2 years ago

ULT ma 4. Write an expression, then evaluate. a. 1/4of the sum of 18 and 6

OlgaM077 [116]

Answer: Required expression: $\dfrac14\times(18+16)$

Result: $\dfrac{17}{2}$

Step-by-step explanation:

Given phrase: $" \dfrac14\text{ of the sum of } 18\text{ and }6. "$

Required expression: $\dfrac14\times(18+16)$ ['+' used to express sum, 'x' used in place of 'of']

Since 18+16 = 34

Then,

$\dfrac14\times(18+16)=\dfrac14\times34 \\\\=\dfrac{1}{2}\times17\ \ \text{[Divide numerator and denominator by 2]}\\\\=\dfrac{17}{2}$

Hence, $\dfrac14\times(18+16)=\dfrac{17}{2}.$

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3 years ago