Question

(8) If the given quadratic equation 2x2+2x+p=0 has equal roots, then p=
(9) If x=3 is one root of the quadratic equation x2-2kx-6=0, then the value of k is​

Answer 1

Answer:

$(8) If \ the \ given \ quadratic \ equation \ 2x^2+2x+p=0 \\ has \ equal \ roots, then \ p=? \\\\ \text{the equation is of the form } ax^2+bx+c=0 \\ a=2,b=2,c=p \\\\=> \underline{Condition \ for \ equal \ roots:} \\ Discriminant,D=b^2-4ac=0 \\\\ 2^2-4(2)(p)=0\\4-8p=0\\8p=4\\p=4/8\\ \boxed{p=\frac{1}{2}}$

$(9) If \ x=3 \ is \ one \ root \ of \ the \ quadratic \ equation \ x^2-2kx-6=0,\\ then \ the \ value \ of \ k \ is \\\\ put \ x=3, \\\\ => (3)^2-2k(3)-6=0 \\ =>9-6k-6=0\\=>3-6k=0\\=>6k=3\\=>k=3/6 \\ => \boxed{k=\frac{1}{2}}$