root of the equation x² 3x+q=0 is twice the other
Then the value of q is?
Answers
Correct question :
One of the root of the quadratic equation x² - 3x + q = 0 is twice of the other , then find the value of q .
Answer :
q = 2
Note:
★ The possible values of the variable which satisfy the equation are called its roots or solutions .
★ A quadratic equation can have atmost two roots .
★ The general form of a quadratic equation is given as ; ax² + bx + c = 0
★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;
• Sum of roots , (α + ß) = -b/a
• Product of roots , (αß) = c/a
Solution :
Here ,
The given quadratic equation is ;
x² - 3x + q = 0 .
Comparing the given quadratic equation with the general quadratic equation
ax² + bx + c = 0 , we have ;
a = 1
b = -3
c = q
Also ,
It is given that , one of the root of the given quadratic equation is twice the other .
Thus ,
Let r and 2r be the two roots of the given quadratic equation .
Now ,
=> Sum of roots = -b/a
=> r + 2r = -(-3)/1
=> 3r = 3
=> r = 3/3
=> r = 1
Now ,
=> Product of roots = c/a
=> r•2r = q/1
=> 2r² = q
=> 2•1² = q
=> 2 = q
=> q = 2
Hence , q = 2
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Probable Question :
One of the root of the quadratic equation x² + 3x + q = 0 is twice of the other , then find the value of q .
Solution :
Here ,
The given quadratic equation is ;
x² + 3x + q = 0 .
Comparing the given quadratic equation with the general quadratic equation
ax² + bx + c = 0 , we have ;
a = 1
b = 3
c = q
Also ,
It is given that , one of the root of the given quadratic equation is twice the other .
Thus ,
Let r and 2r be the two roots of the given quadratic equation .
Now ,
=> Sum of roots = -b/a
=> r + 2r = -3/1
=> 3r = -3
=> r = -3/3
=> r = -1
Now ,
=> Product of roots = c/a
=> r•2r = q/1
=> 2r² = q
=> 2•(-1)² = q
=> 2 = q
=> q = 2