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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 31
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If calphac and cbetac are the roots of cx^2-7x+10=0c, what is the value of (alpha-1)(beta-1)c?

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Answer and explanation

Correct answer: 4

For a quadratic equation cax^2+bx+c=0c, the sum of the roots is alpha+beta=-b/ac and their product is alphabeta=c/ac. Hence, here alpha+beta=7c and alphabeta=10c. Therefore, (alpha-1)(beta-1)=alphabeta-alpha-beta+1=10-7+1=4c. Exam tip: For expressions involving roots, first find their sum and product instead of solving for the roots individually.

Related tags

Roots Of Quadratic EquationVieta FormulasTransformed ExpressionSum And Product Of Roots

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

For a quadratic equation cax^2+bx+c=0c, the sum of the roots is alpha+beta=-b/ac and their product is alphabeta=c/ac. Hence, here alpha+beta=7c and alphabeta=10c. Therefore, (alpha-1)(beta-1)=alphabeta-alpha-beta+1=10-7+1=4c. Exam tip: For expressions involving roots, first find their sum and product instead of solving for the roots individually.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.

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