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If one root of the equation is 2, find the other root of the equation x2−5x+6 A. 5 B. 3 C. 7 D. 8

If one root of the equation is 2, find the other root of the equation x2−5x+6
A. 5
B. 3
C. 7
D. 8

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
10 days ago
Hint: Here, one root is given for the quadratic equation x2−5x+6=0. Now, we can find the other root by the formula for sum and product of the roots. If α and β are the two roots of the quadratic equation ax2+bx+c=0 then the sum and product of the roots are given by the formula: α+β=−ba and αβ=ca. Complete step-by-step answer: Here, given the quadratic equation x2−5x+6=0 and one root of the equation is 2. Now, we have to find the other root of the equation. We know that a quadratic equation in the variable x is an equation of the form ax2+bx+c=0 where a,b,c are real numbers a≠0 We also know that a quadratic equation has two roots. The roots of the equation are given by the formula: −b±b2−4ac−−−−−−−√2a. For the quadratic equation ax2+bx+c=0, if α and β are the two roots then the sum of the roots is given by the formula: α+β=−ba Hence, the product of the roots is given by the formula: αβ=ca Here, corresponding to the quadratic equation ax2+bx+c=0, we have the quadratic equation x2−5x+6=0 where a=1,b=−5,c=6 Here, one root is given which is 2. Now to find the other root consider the sum of the roots of the quadratic equation: α+β=−ba2+β=−(−5)12+β=512+β=5 Now, by taking 2 to the right side it becomes -2, hence, we get: β=5−2β=3 Hence, we will get the other root as 3. Therefore, the two roots of the equation are 2 and 3. Hence, the correct answer for this question is option (b). Note: Here, we can also find the roots by directly substituting the values of a,b and c in the formula −b±b2−4ac−−−−−−−√2a. Otherwise, you can find the roots by splitting the terms and finding the factors, if you don’t know the formula for sum and product of the roots.

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