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# Find the Zeroes of the Following Quadratic Polynomials and Verify the Relationship Between the Zeroes and the Coefficients F(X)=X^2-(Sqrt3+1)X+Sqrt3 - CBSE Class 10 - Mathematics

ConceptRelationship Between Zeroes and Coefficients of a Polynomial

#### Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

f(x)=x^2-(sqrt3+1)x+sqrt3

#### Solution

f(x)=x^2-(sqrt3+1)x+sqrt3=x^2-sqrt3-x+sqrt3

=x(x-sqrt3)-1(x_sqrt3)

=(x-1)(x-sqrt3)

Zeroes of the polynomials are 1 and sqrt3

Sum of zeroes ="-(coefficient of x)"/("coefficient of "x^2)=(-(-sqrt3-1))/1

1+sqrt3=sqrt3+1

Product of zeroes ="constant term"/"coefficient of"x^2=sqrt3/1

1xxsqrt3=sqrt3

sqrt3=sqrt3

Hence, relationship verified

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Solution Find the Zeroes of the Following Quadratic Polynomials and Verify the Relationship Between the Zeroes and the Coefficients F(X)=X^2-(Sqrt3+1)X+Sqrt3 Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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