Q8 of 49 Page 1

Find the value of m so that the quadratic equation mx(5x – 6) + 9 = 0 has two equal roots.

mx(5x-6) + 9 =0

5mx2-6mx + 9=0


This is a quadratic equation of form ax2 + bx + c=0


Where a=5m, b=-6m, c=9


For equal roots, D=0


D=b2-4ac=0


Substituting the values of a,b and c


(-6m)2-4(5m)(9)=0


⇒ 36m2-180m=0


⇒ 36(m2-5m)=0


⇒ m(m-5)=0


There are two possible values of m, m=0 and m=5


But if m=0, then the equation will not remain quadratic,
 ∴ m=5.


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