Question

The product of roots of the equation 3x² - 5mx + (m? + 5) = 0 is 2 then 'm' is​

Answer 1

Let α be the common root

Then 3α2−2mα−4=0 and α2−4mα+2=0

By cross-multiplication, we get

−4m−16mα2=−4−6α=−12m+2m1

⇒−20mα2=−10α=−10m1⇒2mα2=1α=m1

From first two terms, α=2m and from the last two terms, α=m1

∴2m=m1

∴2m2=1

∴m=±21

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