Question

the polynomial equation 2x²+kn +3=0 has two equal
roots , then the value of K is?
(a+-√6. (b) +-4. (c)+-3√2 (d) +-2√6 The sum of the roots of the quadric equation
3x²-9x +5=0 is?
a) 3 (b)6
(c)-3
(d)2​

Answer 1

$\huge\fbox\red{answer}$

${\textsf{if a quadratic equation has real and equal roots the the value of its discriminant}}$

$\sf {D \: which \: is \: b^2 –4ac=0 }$

${\text{\sf{In these equation :-}}} \\ {\sf{2x^{2} + kx+3=0}}\\{\sf{here,}}\\{\sf{a(co-efficient \: of\: x^{2} )=2}} \\ {\sf{b(co-efficient of x)=k}}\\{\sf{c(the\: constant\: value)=3}} \\ \\ {\sf{D=b^{2} - 4ac}} \\{\sf{D=k^{2} - 4 \times 2\times3}} \\{\sf{D=k^{2} -24}} \\ \\ {\sf{FOR\: EQUAL\: ROOTS\: 'D'\: MUST\: BE\: EQUAL\: TO\: ZERO}}\\{\sf{D=0 }}\\{\sf{k^{2} -24=0}}\\\\{\text{\sf{ADDING 24 TO BOTH SIDES}}}\\{\sf{k^{2} -24+24=24}}\\{\sf{k^{2} =24}}\\{\sf{k=\sqrt{24} }}\\ \sf k = \pm 2 \sqrt{6}$