If (1) is a root of (2x^2-3x+m=0) then what is the value of (m)?
Answer and explanation
Correct answer: (1)
If a number is a root of an equation, substituting that number into the equation must make the result zero. Here the given root is \(x=1\). Substitute it into \(2x^2-3x+m=0\): \(2(1)^2-3(1)+m=0\), so \(2-3+m=0\). This simplifies to \(m-1=0\), giving \(m=1\), which is option B.
The important point is that the root condition is checked by direct substitution. No quadratic formula or factorisation is needed. Testing the result, the equation becomes \(2x^2-3x+1=0\), and at \(x=1\) its value is \(2-3+1=0\). Thus the supplied answer is correct and the calculation is complete.
Frequently asked questions
What is the correct answer to this question?
(1)
Why is this the correct answer?
If a number is a root of an equation, substituting that number into the equation must make the result zero. Here the given root is \(x=1\). Substitute it into \(2x^2-3x+m=0\): \(2(1)^2-3(1)+m=0\), so \(2-3+m=0\). This simplifies to \(m-1=0\), giving \(m=1\), which is option B.
The important point is that the root condition is checked by direct substitution. No quadratic formula or factorisation is needed. Testing the result, the equation becomes \(2x^2-3x+1=0\), and at \(x=1\) its value is \(2-3+1=0\). Thus the supplied answer is correct and the calculation is complete.
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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