Use the discriminant to describe the type and number of roots of 9x2+3x−2=0. The quadratic equation has two distinct real number roots. The quadratic equation has one imaginary and one real number root. The quadratic equation has one real number root. The quadratic equation has two complex number roots.

Question

Use the discriminant to describe the type and number of roots of 9x2+3x−2=0.  The quadratic equation has two distinct real number roots.  The quadratic equation has one imaginary and one real number root.  The quadratic equation has one real number root.  The quadratic equation has two complex number roots.

Antum1978 · Accepted Answer

Step 1 basic information  Let us assume the quadratic equation  ax2+bx+c=0  then roots of the above equation is given by  x=−b±D2a  where D is the discriminant given as  D=b2−4ac  If the equation have  D&amp;gt;0, then equation have two real and distinct roots.  D=0, then equation have one root with repetition.  D&amp;lt;0, then equation have two imaginary roots.  Given 9x2+3x−2=0−1  on comporing with ax2+bx+c=0  we get  a=9,b=3,c=−2  Discriminant D=b2−4ac  D=(3)2−4(9)(−2)  =92+(8)(9)  =81+72=153  D=153&amp;gt;0  ⇒ eguatin has aworal and distinct roots

Use the discriminant to describe the type and number of

Answered question

Answer & Explanation

New Questions in Algebra I