Find the value of m for which (m + 5)x2 + (m + 5)x - 1 = 0 has equal roots.
Answers
Answer:
a=m+5, b=m+5, c=(-1)
Step-by-step explanation:
therefore for equal roots D=0
D=b^2-4ac=0
(m+5)^2-4(m+5)(-1)
m^2+10m+25+4m+20=0
m^2+14m+45=0
m^2+9m+5m+45=0
m(m+9)+5(m+9)=0
(m+5)(m+9)=0
m= - 5
m= - 9
Given,
A quadratic equation: (m + 5)x^2 + (m + 5)x - 1 = 0
It had both roots equal.
To find,
The value of m.
Solution,
We can simply solve this mathematical problem using the following process:
Mathematically,
In a quadratic equation: ax^2 + bx + c = 0, the nature of its roots is determined by the value of discriminant D = (b^2-4ac), as follows:
a) if D>0, then real and distinct roots
b) if D=0, then real and equal roots
c) if D<0, then complex and distinct roots
{Statement-1}
For the given quadratic equation,
The value of a = (m+5)
The value of b = (m+5)
The value of c = (-1)
Now, according to the question and statement-1;
The given quadratic equation has both equal roots
=> Discriminant value of the given quadratic equation = 0
=> D = b^2-4ac = 0
=> b^2 = 4ac
=> (m+5)^2 = 4(m+5)(-1)
=> (m+5) = -4
=> m = -9
Hence, the value of m is equal to (-9).