Identify the two numbers whose sum and product are 4 and 8 respectively
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Answer:
⇒ Sum of the zeros =
3
−8
⇒ Product of zeros =
3
4
⇒ x
2
−(Sumofzeros)x+(Productofzeros)=0
⇒ x
2
−(
3
−8
)x+(
3
4
)=0
⇒ x
2
+
3
8
x+
3
4
=0
⇒ 3x
2
+8x+4=0
∴ The required quadratic equation is 3x
2
+8x+4=0
Now, we are going to find zeros,
⇒ 3x
2
+8x+4=0
⇒ 3x
2
+6x+2x+4=0
⇒ 3x(x+2)+2(x+2)=0
⇒ (x+2)(3x+2)=0
⇒ x+2=0 and 3x+2=0
∴ x=−2,
3
−2
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