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If the sum of the zeroes of the polynomial p(x) = (p
2
– 23)x
2
– 2x – 12 is 1, then p takes the value?
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If the sum of the zeroes of the polynomial p(x) = (p 2 – 23)x 2 – 2x –...
Sum of Zeroes of the Polynomial
The sum of the zeroes of a polynomial is given by the formula: Sum of zeroes = -b/a, where the polynomial is in the form ax^2 + bx + c.

Finding the Sum of Zeroes of p(x)
Given polynomial p(x) = (p^2 – 23)x^2 – 2x – 12. Here, a = (p^2 – 23), b = -2, and c = -12.
Sum of zeroes = -(-2)/(p^2 – 23) = 2/(p^2 – 23).
Given that the sum of the zeroes is 1, we have:
2/(p^2 – 23) = 1.
Solving for p, we get:
2 = p^2 – 23.
p^2 = 25.
p = ±5.

Finding the Value of p
As we have two possible values for p, p = 5 or p = -5.
Therefore, the polynomial p(x) can take the value of either 5 or -5.

Conclusion
In conclusion, the polynomial p(x) = (p^2 – 23)x^2 – 2x – 12 can take the value of either 5 or -5, depending on the value of p.
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If the sum of the zeroes of the polynomial p(x) = (p 2 – 23)x 2 – 2x – 12 is 1, then p takes the value?
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