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Find the zeroes of the quadratic polynomial 6x²-3-7x and verify the relationship between the zeroes and coefficients.Explanation must ✓ Steps needed ✓ |
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Answer» answer is ATTACHED above also Given f(x) = 6x2 – 7x – 3 To FIND the zeros Let us put f(x) = 0 ⇒ 6x2 – 7x – 3 = 0 ⇒ 6x2 – 9x + 2x – 3 = 0 ⇒ 3x(2x – 3) + 1(2x – 3) = 0 ⇒ (2x – 3)(3x + 1) = 0 ⇒ 2x – 3 = 0 x = 3/2 ⇒ 3x + 1 = 0 ⇒ x = -1/3 It GIVES us 2 zeros, for x = 3/2 and x = -1/3 Hence, the zeros of the quadratic equation are 3/2 and -1/3. Now, for verification Sum of zeros = – coefficient of x / coefficient of x2 3/2 + (-1/3) = – (-7) / 6 7/6 = 7/6 Product of roots = CONSTANT / coefficient of x2 3/2 x (-1/3) = (-3) / 6 -1/2 = -1/2 Therefore, the relationship between zeros and their coefficients is verified. |
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