Q

# Can someone help me with this, - Complex numbers and quadratic equations - JEE Main-2

Let $f\left ( x \right )= 2x^{2}+ax+2$. Then values of $'a'$ for which $f\left ( x \right )= 0$ doesn't have imaginary roots are

• Option 1)

$\left |a \right |\geq 1$

• Option 2)

$\left |a \right |\geq2$

• Option 3)

$\left |a \right |\geq4$

• Option 4)

$\left |a \right |\geq3$

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$\because f(x)=0$  doesn't have imaginary roots so either roots are real and equals or roots are real and distinct so $D\geq 0$

$\\*\therefore a^{2}-16\geq 0\\*\Rightarrow a\leq -4\cup a\geq 4\\*\Rightarrow \left | a \right |\geq 4$

Quadratic Expression Graph when a> 0 & D > 0 -

Real and distinct roots of

$f\left ( x \right )= ax^{2}+bx+c$

& $D= b^{2}-4ac$

- wherein

Option 1)

$\left |a \right |\geq 1$

This is incorrect

Option 2)

$\left |a \right |\geq2$

This is incorrect

Option 3)

$\left |a \right |\geq4$

This is correct

Option 4)

$\left |a \right |\geq3$

This is incorrect

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