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Coordinate Geometry
Question
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If x2 + px + q = (x + a)(x + b), then factorise x2 + pxy + qy2.

Answer

x2 + px + q = (x + a)(x + b)
⇒ x2+ px + q = x2 + ax + bx + ab
⇒ x2+ px + q = x2 + (a + b)x + ab
Comparing the coefficients, we get
a + b = p    ...(1)
ab = q    ...(2)
∴ x2 + pxy + qy2 = x2 + (a + b)xy + aby2
| Using (1) and (2)
= x2 + axy + bxy + aby2
= x(x + ay) + by(x + ay)
= (x + ay)(x + by).

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Some More Questions From Coordinate Geometry Chapter

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

4x2 - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

x10+ y3 + t50

Write the coefficients of x2 in each of the following:

2 + x2 + x

Write the coefficients of x2 in each of the following:
2 - x2 + x3