Question

Let a, b, c be distinct non-negative numbers and the vectors a + a + c $\hat { \mathbf { k } }$ , + $\hat { \mathbf { k } }$ , c + c + b $\hat { \mathbf { k } }$ lie in a plane, then the quadratic equation ax² + 2cx + b = 0 has –

• A. real and equal roots
• B. real unequal roots
• C. unreal roots
• D. both roots real and positive

Answer 1

Answer: (A)

real and equal roots

Answer 2

$\left| \begin{array} { l l l } a & a & c \\ 1 & 0 & 1 \\ c & c & b \end{array} \right|$ = 0

̃ c² – ab = 0

0 = 4c² – 4ab = 4 (c² – ab) = 0

roots are = – $\frac { 2 \mathrm { c } } { 2 \mathrm { a } }$ = – $\frac { \mathrm { c } } { \mathrm { a } }$ £ 0

So roots are real and equal.