Solve the following equation by factorisation on paper:

12
𝑥
2
+
7
𝑥
−
10
=
0

AND

In this quiz, enter the coefficient of the term with the highest power of x.

(Answer in quiz: 1 mark)
(Written answer: 2 marks)

Question

Solve the following equation by factorisation on paper:

12
𝑥
2
+
7
𝑥
−
10
=
0

AND

In this quiz, enter the coefficient of the term with the highest power of x.

(Answer in quiz: 1 mark)
(Written answer: 2 marks)

BlackTom AI · Accepted Answer

We start by understanding what is being asked: solve the equation 12x^2 + 7x - 10 = 0 by factorisation, and then in the quiz input the coefficient of the term with the highest power of x.

First, identify the structure of the quadratic: a x^2 + b x + c with a = 12, b = 7, c = -10. The coefficient of the highest power of x is the leading coefficient, which is 12. This is the number that multiplies x^2 in the expanded form.

Next, attempt to factor the quadratic into (px + q)(rx + s) where pr = 12 and qs = -10, and the cross-term p s + q r equals 7. Checking factor pairs of 12 and -10, we find that (4x + 5)(3x - 2) expands to 12x^2 + 7x - 10, since 4x*3x gives 12x^2, 4x*(-2) and 5*(3x) give -8x + 15x = 7x, and 5*(-2) gives -10.

Therefore, the factored form is (4x + 5)(3x - 2) = 0, which yields the roots x = -5/4 and x = 2/3. The crucial point for the quiz prompt, however, is recognizing that the coefficient of the x^2 term in the original quadratic is 12, i.e., the leading coefficient.

If you were to list the roots for completeness: x = -5/4 or x = 2/3. But for the quiz’s asked value, the leading coefficient remains 12, which is the number you would input for the coefficient of the term with the highest power of x.

Solve the following equation by factorisation on paper: 12 𝑥 2 + 7 𝑥 − 10 = 0 AND In this quiz, enter the coefficient of the term with the highest power of x. (Answer in quiz: 1 mark) (Written answer: 2 marks)

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