Question #18cf4

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Answer 1 · 2017-03-27T07:46:39

$(a) : p=40/363, and, (b) :" the two roots are, "2/33 and 20/33.$

We know that, if $gamma and delta$ are the Roots of the

Quadr. Eqn. # : ax^2+bx+c=0, then,

$gamma+delta=-b/a, and, gammadelta=c/a.........(star)$

Let the roots of the given quadr. eqn. be, $alpha and beta.$

We are given that, one root is $10$ times the other.

We take, $beta=10alpha.....(1).$

Applying $(star)," we get, "alpha+beta=-(-2/3)=2/3.$

$"Then, "(1) rArr alpha+10alpha=11alpha=2/3, or, alpha= 2/33.$

Accordingly, $beta=10alpha=20/33.$

Again, by $(star), alpha*beta=p/3.$

$:. p=3alpha*beta=3(2/33)(20/33)=40/363.$

Thus, $(a) : p=40/363, and, (b) :" the two roots are, "2/33 and 20/33.$

Enjoy Maths.!