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India
Class IX

Multiplicity of a Root

Interactive practice questions

Consider the polynomial $P\left(x\right)=\left(x+6\right)^3\left(x-3\right)\left(x+9\right)$P(x)=(x+6)3(x3)(x+9).

a

For the equation $P\left(x\right)=0$P(x)=0, what is the multiplicity of the root $x=-6$x=6?

b

For the equation $P\left(x\right)=0$P(x)=0, what is the multiplicity of the root $x=-9$x=9?

Easy
< 1min

Which of the following equations has a root of multiplicity $4$4?

Easy
< 1min

Which of the following equations have a root of multiplicity $3$3?

Easy
1min

Consider the polynomial $P\left(x\right)=x^3-15x^2+72x-108$P(x)=x315x2+72x108.

Easy
5min
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Outcomes

9.A.P.1

Definition of a polynomial in one variable, its coefficients, with examples and counterexamples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial/equation.

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