Write the following equations in the form ax2 + bx + c = 0, then write

1.	Write the following equations in the form ax2 + bx + c = 0, then write the values of a, b, c for eachi. 2y = 10 – y2ii. (x – 1)2 = 2x + 3iii. x2 + 5x = – (3 – x)
Answer» i. 2y – 10 – y² ∴ y² + 2y – 10 = 0 Comparing the above equation with ay² + by + c = 0, we get a = 1, b = 2, c = -10 ii. (x – 1)² = 2x + 3 ∴ x² – 2x + 12x + 3 x² – 2x + 1 – 2x – 30 ∴ x² – 4x – 2 = 0 Comparing the above equation with ax² + bx + c = 0, we get a = 1, b = -4, c = -2 iii. x² + 5x = – (3 – x) ∴ x² + 5x = -3 + x ∴ x² + 5x – x + 3 = 0 ∴ x² + 4x + 3 = 0 Comparing the above equation with ax² + bx + c = 0, we get a = 1, b = 4, c = 3

Write the following equations in the form ax2 + bx + c = 0, then write the values of a, b, c for eachi. 2y = 10 – y2ii. (x – 1)2 = 2x + 3iii. x2 + 5x = – (3 – x)

Answer»

i. 2y – 10 – y²

∴ y² + 2y – 10 = 0

Comparing the above equation with

ay² + by + c = 0, we get

a = 1, b = 2, c = -10

ii. (x – 1)² = 2x + 3

∴ x² – 2x + 12x + 3

x² – 2x + 1 – 2x – 30

∴ x² – 4x – 2 = 0

Comparing the above equation with

ax² + bx + c = 0, we get

a = 1, b = -4, c = -2

iii. x² + 5x = – (3 – x)

∴ x² + 5x = -3 + x

∴ x² + 5x – x + 3 = 0

∴ x² + 4x + 3 = 0

Comparing the above equation with

ax² + bx + c = 0, we get

a = 1, b = 4, c = 3