1. Find the values of k for which the quadratic
equation 4x2 + 5kx + 25 = 0 has equal roots.
Answers
Answer:
The value of k= +4,-4
Step-by-step explanation:
Equation-=> 4x²+5kx+25
Given-:
The equation has equal and real roots
To find-:
Value of K
Solution-:
As the equation has equal and real
roots. So, rhe discriminant will be zero
Discriminant= b²-4ac
where a=4,b=5k and c=25
Now,
=>B²-4ac=0
=>(5k)²-4*4*25=0
=>25k²-400=0
=>25k²=400
=>k²=16
=>k= +4,-4
Question:
Find the value of k for which the quadratic equation 4x² + 5kx + 25 = 0 has equal roots.
Answer:
k = ± 4
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 .
• 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 ;
4x² + 5kx + 25 = 0 .
Clearly , we have ;
a = 4
b = 5k
c = 25
We know that ,
The quadratic equation will have real and equal roots if its discriminant equal to zero .
=> D = 0
=> (5k)² - 4•4•25 = 0
=> 25k² - 16•25 = 0
=> 25•(k² - 16) = 0
=> k² - 16 = 0
=> k² = 16
=> k = √16
=> k = ± 4
Hence,
Hence,The required values of k are ± 4 .