Question

An equation has solutions of m = –5 and m = 9. Which could be the equation? (m + 5)(m – 9) = 0 (m – 5)(m + 9) = 0 m2 – 5m + 9 = 0 m2 + 5m – 9 = 0

Answer 1

Answer:

(m+5)(m-9) =0 is correct

Explanation:

Given m=-5 and m = 9 are solutions of a quadratic equation.

Then,

m+5 = 0 Or m-9 = 0 are factors of the equation.

=> (m+5)(m-9)=0 is the required

quadratic equation.

Or

Form of the quadratic equation :

m²-(sum of the roots)m+product of the roots = 0

=> m²-(-5+9)m+(-5)×9=0

=> m²-4m-45=0

••••

Answer 2

Equation is (m + 5)(m – 9) = 0 for solutions m = -5 and m = 9

Solution:

Zeroes or roots of equation are m = -5 and m = 9

Roots of equation is given then the equation is a x^{2}+b x+c=0  

To find the values of a, b and c, we take the sum and product of the roots

$\begin{array}{l}{\alpha+\beta=4} \\ \\{\alpha \beta=-45} \\ \\{4=-\frac{b}{a}} \\ \\{-45=\frac{c}{a}}\end{array}$

Taking the value of b and c in terms of a

-b = 4a

c = -45a    

Forming the equation, we get

$a m^{2}-4\ a m-45 a = 0$

Now as we can see the equation forming (m+5)( m-9) has roots m = –5 and m = 9.  

a((m+5)( m-9))=0  

After keeping a = 1, we can see that m = -5, 9

a=1

m = -5,9  

Equation is (m + 5)(m – 9) = 0