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Coordinate Geometry

Question
CBSEENMA9001787
Wired Faculty App

Determine the value of ‘b’ for which the polynomial 5x3 - x2 + 4x + b is divisible by 1 - 5x.

Solution

Let p(x) = 5x3 - x2 + 4x + b
1 - 5x = 0
rightwards double arrow space space space space space space space space 5 straight x space equals space 1 space space space rightwards double arrow space space space straight x space equals space 1 fifth
therefore  The zero of 1 - 5x is 1 fifth
If p(x) is divisivle by 1 - 5x, then straight p open parentheses 1 fifth close parentheses equals 0
                                         | By Factor Theorem
rightwards double arrow space 5 open parentheses 1 fifth close parentheses cubed minus open parentheses 1 fifth close parentheses squared plus 4 open parentheses 1 fifth close parentheses plus straight b equals 0 rightwards double arrow space space 1 over 25 minus 1 over 25 plus 4 over 5 plus straight b equals 0 rightwards double arrow space space space 4 over 5 plus straight b equals 0 rightwards double arrow space space space space straight b space equals space minus 4 over 5.

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

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