Find the discriminant of each of the following equations : ( i ) 2 x 2 − 7 x + 6 = 0 ; ( i i ) 3 x 2 − 2 x + 8 = 0 ; ( i i i ) 2 x 2 − 5 2 x + 4 = 0 ; ( i v ) 3 x 2 + 2 2 x − 2 3 = 0 ; ( v ) ( x − 1 ) ( 2 x − 1 ) = 0 ; ( v i ) 1 − x = 2 x 2

Question

Find the discriminant of each of the following equations :    (  i  )  2      x    2    −  7  x  +  6  =  0  ;    (  i  i  )  3      x    2    −  2  x  +  8  =  0  ;    (  i  i  i  )  2      x    2    −  5      2    x  +  4  =  0  ;    (  i  v  )      3        x    2    +  2      2    x  −  2      3    =  0  ;    (  v  )  (  x  −  1  )  (  2  x  −  1  )  =  0  ;    (  v  i  )  1  −  x  =  2      x    2

Kelton Sanders · Accepted Answer

(  i  )  2      x    2    −  7  x  +  6  =  0The quadratic equation provided is expressed as   a      x    2    +  b  x  +  c  =  0Where, a=2,b=−7,c=6Therefore, discriminant   D  =      b    2    −  4  a  c    =      7    2    −  4  ×  2  ×  6    =  49  −  48    ∴  D  =  1   (  i  i  )  3      x    2    −  2  x  +  8  =  0 Comparing with   a      x    2    +  b  x  +  c  =  0, we geta=3,b=−2,c=8Thus, the discriminant   D  =      b    2    −  4  a  c  =  (  −  2      )    2    −  (  4  ×  3  ×  8  )    =  4  −  96    ∴  D  =  −  92  (  i  i  i  )  2      x    2    −  5      2    x  +  4  =  0Where   a  =  2  ,  b  =  −  5      2    ,  c  =  4  D  =      b    2    −  4  a  c    =  (  −  5      2        )    2    −  4  ×  2  ×  4    =  50  −  32    ∴  D  =  18   i  v  )      3        x    2    +  2      2    x  −  2      3    =  0    a  =      3    ,  b  =  2      2    ,  c  =  −  2      3      D  =      b    2    −  4  a  c    =  (  2      2        )    2    −  4  ×      3    ×  −  2      3      =  8  +  24    ∴  D  =  32   (  v  )  (  x  −  1  )  (  2  x  −  1  )  =  0    2      x    2    −  x  −  2  x  +  1  =  0    2      x    2    −  3  x  +  1  =  0 Where a=2,b=−3,c=1  D  =      b    2    −  4  a  c    =  (  −  3      )    2    −  4  ×  2  ×  1    =  9  −  8    ∴  D  =  1 (vi)   1  −  x  =  2      x    2  Given equation is written as   2      x    2    +  x  −  1  =  0Where a=2,b=1,c=−1  D  =      b    2    −  4  a  c    =      1    2    −  (  4  ×  2  ×  −  1  )    =  1  +  8    ∴  D  =  9

Find the discriminant of each of the following equations : (i) 2x^2−7x+6=0; (ii) 3x^2−2x+8=0; (iii) 2x^2−5 sqrt(2)x+4=0; (iv) sqrt(3)x^2+2 sqrt(2)x−2 sqrt(3)=0; (v) (x−1)(2x−1)=0; (vi) 1−x=2x^2

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