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. About the author Sophia
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> Reply
[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] Reply
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>
[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]