Question

the roots of the quadratic equation x²-5x-6=0 are​

Answer 1

Answer:

-2 & -3 are the roots of quadratic equation x2 + 5x + 6 = 0.

Answer 2

Use x² + (a+b)x + (ab) = (x+a)(x+b)

Now, we need to find a and b, for that see the sign of c i.e. -6 .... its '-' so when we will separate -5x into ax and bx the equation would be of SUBTRACTION..... means

x² + ( a -b)x -(ab)...... but -5 is also negative so....

equation must be x² -(a-b)x -(ab) = (x-a)(x+b)

So, to find a and b we must see the factors of 6 i.e. 1×6 and 2×3

when 6-1 = 5..... as we needed..... for 5x and as a difference as (ab) = -6....

so, x² -(6-1)x -6 = 0

x² -6x +x-6 = 0

x(x-6) +1(x-6) = 0

(x+1)(x-6) = 0

So its zeroes are, x+1 = 0 => x = -1......., x-6=0 => x= 6.....

so 2 zeroes are x = -1,6

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