Question 1:
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
Therefore, the zeroes of x2 ─2x─8 are 4 and −2.
Sum of zeroes =
Product of zeroes
The value of 4s2 − 4s + 1 is zero when 2s − 1 = 0, i.e.,s=1/2
Therefore, the zeroes of 4s2 − 4s + 1 are1/2and1/2.
Sum of zeroes =
Product of zeroes
The value of 6x2 − 3 − 7x is zero when 3x + 1 = 0 or 2x − 3 = 0, i.e., -1/3 or 3/2
Therefore, the zeroes of 6x2 − 3 − 7x are
.Sum of zeroes =
Product of zeroes =
The value of 4u2 + 8u is zero when 4u = 0 or u + 2 = 0, i.e., u = 0 or u = −2
Therefore, the zeroes of 4u2 + 8u are 0 and −2.
Sum of zeroes =
Product of zeroes =
The value of t2 − 15 is zero when t ─ √15 = 0 or t + √15 = 0, i.e., when t = √15 or t = ─ √15
Therefore, the zeroes of t2 − 15 are √15 and ─ √15.
Product of zeroes =
The value of 3x2 − x − 4 is zero when 3x − 4 = 0 or x + 1 = 0, i.e., when x = 4/3 or x = −1
Therefore, the zeroes of 3x2 − x − 4 are 4/3 and −1.
Sum of zeroes =
Product of zeroes
Next Q.2