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13.02.2023 03:02
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What are the solutions to 7x^2 + 10x - 3 = x^2 +3x? select all that apply. a. (3/2)

What are the solutions to 7x^2 + 10x - 3 = x^2 +3x? select all that apply.
a. (3/2)
b. (-3/2)
c. (1/3)
d. (-1/3)
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samiiegarciia
samiiegarciia
4,7(63 marks)

when i did the problem i got 0.333 which is just \frac{1}{3} i also got \frac{-3}{2}

Step-by-step explanation:

if you need step ill do that for you just ask in the comments :)

bluebug7316
bluebug7316
4,5(13 marks)

If binomial (3x+2) is  a factor of some polynomial, then number x=-\dfrac{2}{3} is this polynomial's root. Check all polynomials:

A. For the polynomial 6x^3 + 3x^2 + 4x + 2,

6\left(-\dfrac{2}{3}\right)^3 + 3\left(-\dfrac{2}{3}\right)^2 + 4\left(-\dfrac{2}{3}\right) + 2=-\dfrac{16}{9}+\dfrac{4}{3}-\dfrac{8}{3}+2=-\dfrac{10}{9}\neq 0.

B. For the polynomial 12x^2 + 15x + 8x + 10,

12\left(-\dfrac{2}{3}\right)^2 + 23\left(-\dfrac{2}{3}\right) + 10=\dfrac{16}{3}-\dfrac{46}{3}+10=0.

C. For the polynomial 18x^3-12x^2 + 9x-6,

18\left(-\dfrac{2}{3}\right)^3 -12\left(-\dfrac{2}{3}\right)^2 + 9\left(-\dfrac{2}{3}\right) -6=-\dfrac{16}{3}-\dfrac{16}{3}-6-6\neq 0.

D. For the polynomial 21x^4 + 7x^3 + 6x + 2,

21\left(-\dfrac{2}{3}\right)^4 +7\left(-\dfrac{2}{3}\right)^3 +6\left(-\dfrac{2}{3}\right) +2=\dfrac{112}{27}-\dfrac{56}{27}-4+2\neq 0.

correct choice is B

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