Question

Q1.factorise
5x^2+3x+6 and x^2+2x-25​

Answer 1

Explanation:

5x²+3x+6

It is in the form of a quadratic equation hence,it can be factorise.

How to factorise

5x²+3x+6

The coefficient of x² is 5

3x is a middle term and its coefficient is 3.

and the constant" is +6

Step-1 : Multiply the coefficient of x² by the constant 5×6=30

Step-2 : Find two factors of 30 whose sum is equal to the coefficient of the middle term, which is 3.

No two such factors can be found !!

we can sove by using quadratic formula :

x=-b±√b²-4ac÷2a

Here, a= 5,b= 3 & c= 6

=>x= -3±√3²-4(5)(6)/2(5)

=>x=-3±√9-120/10

=>x=-3±√-111/10

Here,the discriminant b²-4ac is <0

So,there would be two complex roots.

x=-3±√111 i /10

x=-3±√111 i /10x= -3/10 ± √111 i /10

Further solved :

x= -0.3+1.05357 i

x= -0.3-1.05357 i

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x²+2x-25

No factor can be found so,it's also be solved through quadratic formula:

a=1,b= 2 c= -25

=>x= -2±√2²-4(1)(-25)/2(1)

=>x= -2±√4+100/2

=>x= -2±√104/2

Here,the discriminant b²-4ac is >0

So,there will be two real roots

=>x= -2±2√26/2

=>x=-2/2±2√26/2

x= -1±√26

further solved :

x=4.09902

x=- 6.09902