The quadratic equation with real co-efficients one of whose complex roots has the real part 12 and modulus 13 is:

Question

The quadratic equation with real co-efficients one of whose complex roots has the real part 12 and modulus 13 is: (A) x2-12 x+13=0 (B) x2-24 x+13=0 (C) x2-24 x+169=0 (D) x2-24 x-169=0

Tardigrade Admin · Accepted Answer

Let the roots be 12+α i; other roots is 12-α i now z overline z =| z |2 ∴ 144+ a 2=169 ⇒ α= ± 5 text Hence roots are 12 ± 5 i

Q. The quadratic equation with real co-efficients one of whose complex roots has the real part 12 and modulus 13 is:

$x^{2} - 12 x + 13 = 0$

$x^{2} - 24 x + 13 = 0$

$x^{2} - 24 x + 169 = 0$

$x^{2} - 24 x - 169 = 0$

Let the roots be $12 + α i$ ; other roots is $12 - α i$ now $z \overline{z} = ∣ z ∣^{2}$
$∴ 144 + a^{2} = 169 \Rightarrow α = \pm 5$
$Hence roots are 12 \pm 5 i$

Q. The quadratic equation with real co-efficients one of whose complex roots has the real part 12 and modulus 13 is:

x2−12x+13=0

x2−24x+13=0

x2−24x+169=0

x2−24x−169=0

Let the roots be 12+αi; other roots is 12−αi now zz=∣z∣2 ∴144+a2=169⇒α=±5 Hence roots are 12±5i

$x^{2} - 12 x + 13 = 0$

$x^{2} - 24 x + 13 = 0$

$x^{2} - 24 x + 169 = 0$

$x^{2} - 24 x - 169 = 0$

Let the roots be $12 + α i$ ; other roots is $12 - α i$ now $z \overline{z} = ∣ z ∣^{2}$
$∴ 144 + a^{2} = 169 \Rightarrow α = \pm 5$
$Hence roots are 12 \pm 5 i$