8. If each zero of the polynomial x2 + mx + n is three times to the zeroes of 3×2 -5x + 2, find the
values of m and n.
​

1 thought on “8. If each zero of the polynomial x2 + mx + n is three times to the zeroes of 3×2 -5x + 2, find the<br />values of m and n.<br />​”

1. SOLUTION

   GIVEN

   If each zero of the polynomial x² + mx + n is three times to the zeroes of 3x² – 5x + 2

   TO DETERMINE

   The value of m and n

   EVALUATION

   Here the given polynomial is 3x² – 5x + 2

   Now we find the roots of the polynomial

   For Zero of the polynomial 3x² – 5x + 2 we have

   [tex] \displaystyle \sf{3 {x}^{2} – 5x + 2 = 0 }[/tex]

   [tex] \displaystyle \sf{ \implies \: 3 {x}^{2} – 3x – 2x + 2 = 0 }[/tex]

   [tex] \displaystyle \sf{ \implies \: 3x(x – 1) – 2(x – 1) = 0 \: }[/tex]

   [tex] \displaystyle \sf{ \implies \: (x – 1) (3x – 2) = 0 \: }[/tex]

   [tex] \displaystyle \sf{ (x – 1) = 0 \: \: gives \: \: x = 1}[/tex]

   [tex] \displaystyle \sf{ (3x – 2) = 0 \: \: gives \: \: x = \frac{2}{3} }[/tex]

   Therefore roots of the quadratic polynomial 3x² – 5x + 2 are [tex] \displaystyle \sf{ 1 \: \: and \: \: \frac{2}{3} }[/tex]

   Now it is given that each zero of the polynomial x² + mx + n is three times to the zeroes of 3x² – 5x + 2

   Therefore roots of the quadratic polynomial x² + mx + n are [tex] \displaystyle \sf{ 3 \: \: and \: \: 2}[/tex]

   Now the quadratic polynomial whose roots are 3 , 2 are

   [tex] \sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }[/tex]

   [tex] = \sf{ {x}^{2} – (3 + 2)x + (3 \times 2) }[/tex]

   [tex] = \sf{ {x}^{2} – 5x + 6 }[/tex]

   Now Comparing with x² + mx + n we get

   m = – 5 & n = 6

   ━━━━━━━━━━━━━━━━

   Learn more from Brainly :-

   1. find the equation that formed by increasing each root of 2x²-3x-1=0by 1

   https://brainly.in/question/33063519

   2. find the equation that formed by squaring each root of the equation x²+3x-2=0

   https://brainly.in/question/33064705

   Reply