If the sum of the zeros of the polynomial p(x) = (a²+a)x²+ 45x + 6a is reciprocal of the other, find the value of a.​

2 thoughts on “If the sum of the zeros of the polynomial p(x) = (a²+a)x²+ 45x + 6a is reciprocal of the other, find the value of a.​”

1. Answer:

   Productofzeroes=ac</p><p>α×

   α

   1

   =

   a

   2

   +9

   6a

   α×α1

   =a2+96a</p><p>a

   2

   +9

   =6aa2+9

   =6a</p><p>a

   2

   −6a+9

   =0a2−6a+9

   =0</p><p>a

   2

   −3a−3a+9

   =0a2−3a−3a+9

   =0a(a−3)−3(a−3)

   =0a(a−3)−3(a−3)

   =0(a−3)(a−3)

   =0(a−3)(a−3)

   =0

   ⇒a−3=0

   ⇒a=3</p><p>Therefore, Valueofais3.</p><p>

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2. [tex]\Huge\bf\maltese{\underline{\green{Answer°᭄}}}\maltese[/tex]

   [tex]\implies[/tex][tex]\large\bf{\underline{\red{VERIFIED✔}}}[/tex]

   [tex]Product \: of \: zeroes=ac

   \alpha\times\frac{1}{\alpha} \\ \\ =\frac{6a}{a^2+9}α×α1 \\ \\ =a2+96a

   a^2+9 \\ \\ =6aa2+9 \\ \\ =6a

   a^2-6a+9 \\ \\ =0a2−6a+9 \\ \\ =0

   a^2-3a-3a+9 \\ \\ =0a2−3a−3a+9 \\ \\ =0a(a-3)-3(a-3) \\ \\ =0a(a−3)−3(a−3) \\ \\ =0(a-3)(a-3) \\ \\ =0(a−3)(a−3) \\ \\ =0 \\ \\ ⇒ a – 3 = 0 \\ \\ ⇒ a = 3

   Therefore, Value of a is 3.

   [/tex]

   [tex] \boxed{I \:Hope\: it’s \:Helpful}[/tex]

   [tex]{\sf{\bf{\blue{@ℐᴛz ᴅɪɴᴜ࿐}}}}[/tex]

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