Question

Write the following equations in the form ax² + bx + c= 0, then write the values of a, b, c for each equation.
(1) 2y = 10 – y²
(2) (x – 1)² = 2x + 3
(3) x² + 5x = –(3 – x)
(4) 3m² = 2m² – 9
(5) P(3+6p) = –5
(6) x² – 9 = 13

Answer 1

(1) 2y = 10 – y^{2
$$\begin{gathered} \Rightarrow y^2+2y=10 \\ \Rightarrow y^2+2y-10=0 \end{gathered}$$}
So, it is of the form ax² + bx + c = 0 where a = 1, b = 2 and c = −10.

(2) (x – 1)² = 2x + 3
$$\begin{gathered} \Rightarrow \left(x^2-2x+1\right)=2x+3 \\ \Rightarrow x^2-4x-2=0 \end{gathered}$$
So, it is of the form ax² + bx + c = 0 where a = 1, b = −4 and c = −2.

(3) x² + 5x = –(3 – x)
$$\begin{gathered} \Rightarrow x^2+5x+3-x=0 \\ \Rightarrow x^2+4x+3=0 \end{gathered}$$
So, it is of the form ax² + bx + c = 0 where a = 1, b = 4 and c = 3.

(4) 3m² = 2m² – 9
$$\begin{gathered} \Rightarrow 3m^2-2m^2+9=0 \\ \Rightarrow m^2+0m+9=0 \end{gathered}$$
So, it is of the form ax² + bx + c = 0 where a = 1, b = 0 and c = 9.

(5) p(3+6p) = –5
$$\begin{gathered} \Rightarrow 3p+6p^2+5=0 \\ \Rightarrow 6p^2+3p+5=0 \end{gathered}$$
So, it is of the form ax² + bx + c = 0 where a = 6, b = 3 and c = 5.

(6) x² – 9 = 13
$$\begin{gathered} \Rightarrow x^2-9-13=0 \\ \Rightarrow x^2-22=0 \\ \Rightarrow x^2+0x-22=0 \end{gathered}$$
So, it is of the form ax² + bx + c = 0 where a = 1, b = 0 and c = −22.