Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients 

(i) x² – 2x – 8 

(ii) 4s² – 4s + 1 

(iii) 6x² – 3 – 7x 

(iv) 4u² – 8u 

(v) t² – 15 

(vi) 3x² – x – 4

Answer 1

(iv) 4u² – 8u 

= 4u² – 8u + 0 

= 4u (u – 2) 

If 4u = 0, then u = 0 

If u – 2 = 0, then u = 2

∴ Zeroes are 0 and 2

(vi) 3x² – x – 4 

= 3x² – 4x + 3x – 4 

= x(3x – 4) + 1 (3x – 4) 

= (3x – 4) (x + 1) 

If 3x – 4 = 0, then x = \(\frac{4}{3}\)

If x + 1 = 0, then x = -1 

∴ Zeroes are \(\frac{4}{3}\) and -1