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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.!