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Salsk061 [2.6K]
2 years ago
5

For what values of x will the function f(x) = 3x² + 13x - 10 equal zero?

Mathematics
1 answer:
Oduvanchick [21]2 years ago
4 0

Answer:

x = - 5 , x = \frac{2}{3}

Step-by-step explanation:

the values of x that make f(x) zero are the zeros

to find the zeros let f(x) = 0 , that is

3x² + 13x - 10 = 0

consider the factors of the product of  the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = + 13

the factors are + 15 and - 2

use these factors to split the x- term

3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )

3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term

(x + 5)(3x - 2) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = \frac{2}{3}

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Answer:

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Read 2 more answers
What is HB? Triangle Mid-segment Theorem
Scorpion4ik [409]

Answer:

HB = 13

Step-by-step explanation:

In triangle GHJ, points A, B, C are mid points of the sides GH, HJ, GJ respectively.

Therefore by Mid-segment Theorem.

AC = \frac{1}{2}  HJ \\  \\ 3y - 5 =  \frac{1}{2} (4y + 2) \\  \\  3y - 5 =  \frac{1}{2} \times 2 (2y + 1) \\  \\  3y - 5 =  2y + 1\\  \\ 3y - 2y = 5 + 1 \\  \\ y = 6 \\  \\ HJ = 4y + 2  \\  \\  HJ = 4 \times 6 + 2  \\  \\ HJ = 24 + 2  \\  \\ HJ = 26  \\  \\ HB= \frac{1}{2}  HJ \\  \\ HB= \frac{1}{2}   \times 26 \\  \\ \huge \red{ \boxed{ HB= 13}}

7 0
3 years ago
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