find the value of k for which the given quadratic equation is x^2-kx+9=0
Answers
to find the value of k we find discriminant of equation then
k2-4×1×9=0
k2=36
k=+&-6
Hope it will help you
Question:
Find the value of k for which the quadratic equation x² - kx + 9 = 0 has equal roots.
Answer:
k = ± 6
Note:
• An equation of degree 2 is know as quadratic equation .
• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.
• The maximum number of roots of an equation will be equal to its degree.
• A quadratic equation has atmost two roots.
• The general form of a quadratic equation is given as , ax² + bx + c = 0 .
• The discriminant of the quadratic equation is given as , D = b² - 4ac .
• If D = 0 , then the quadratic equation would have real and equal roots .
• If D > 0 , then the quadratic equation would have real and distinct roots .
• If D < 0 , then the quadratic equation would have imaginary roots .
Solution:
The given quadratic equation is ;
x² - kx + 9 = 0
Clearly , we have ;
a = 1
b = -k
c = 9
We know that ,
The quadratic equation will have equal roots if its discriminant is equal to zero .
=> D = 0
=> (-k)² - 4•1•9 = 0
=> k² - 36 = 0
=> k² = 36
=> k = √36
=> k = ± 6