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If one root of the equation x2тИТkx+12=0 is 3, then what is the value of the other root?
2
3
4
5
4
Since the product of roots ╬▒╬▓ is c/a=12/1=12, simply divide 12 by the given root 3 to get the other root directly.
A quadratic equation x2тИТkx+12=0 is provided where one root ╬▒=3.
╬▒├Ч╬▓=acтАЛ
Since the product of roots ╬▒╬▓ is c/a=12/1=12, simply divide 12 by the given root 3 to get the other root directly.
Students often try to find the value of k first by substituting x=3 into the equation, which is unnecessary and time-consuming.
Identify coefficients
The given equation is x2тИТkx+12=0. Comparing this with the standard form ax2+bx+c=0, we have a=1 and c=12.
a=1,c=12
Apply Product of Roots formula
According to Vieta's formulas, the product of the roots ╬▒├Ч╬▓ of a quadratic equation is given by c/a. Let ╬▒=3 and ╬▓ be the other root.
3├Ч╬▓=112тАЛ
Solve for the second root
Solving for ╬▓, we divide the product 12 by the known root 3.
╬▓=312тАЛ=4
C is correct because the product of the roots ╬▒╬▓=12 implies that 3├Ч╬▓=12, resulting in ╬▓=4.
This property of roots (sum =тИТb/a, product =c/a) is a foundational tool not just in Algebra, but also in solving complex polynomial equations in higher-level competitive exams.
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