Question

ii)
The value for the discriminant for the quadratic equation 2x2 - 4x + 5 = 0 is ......
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Answer 1

Question :

Find the value of discriminant

$\sf{2 \: {x}^{2} - 4x + 5 = 0 }$

Solution :

$\sf{2 \: {x}^{2} - 4x + 5 = 0 } \\ \sf{Comparing \:with \: a {x}^{2} + bx + c = 0 , \: we \: get ,} \\ \sf{a = 2 \: , \: b = - 4 \: , \: c = 5} \\ \\ \sf{\: \: \: \: \: \: \: Δ = \: {b}^{2} \: - \: 4 \: a \: c \: } \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Δ = { - 4}^{2} - 4 \times 2 \times 5 } \\ \sf{\: \: \: \: \: Δ = 16 - 8 \times 5} \\ \sf{Δ = 16 - 40} \\ \sf{Δ = - 24\: \: \: \: \: \: }$

Similar Questions :

$\sf \red{ Q1) \: {x}^{2} + 7x - 1 = 0} \\ \\ \sf{{x}^{2} + 7x - 1 = 0} \\ \sf{Comparing \:with \: a {x}^{2} + bx + c = 0 , \: we \: get \: ,} \\ \sf{a = 1, \: b = 7, \: c = - 1} \\ \\ \sf{ \: \: \: \: \: \: \: Δ = {b}^{2} - 4 \: a \: c} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{\: \: \: \: \: \: \: \: \: \: \: Δ = {7}^{2} - 4 \times 1 \times ( - 1)} \\ \sf{\: Δ =49 + 4} \\ \sf{Δ =53 \: \: \: \: \: \: \:}$

$\sf \red {Q2) \: \: \: \: {2 {y}^{2} - 5y + 10 = 0}} \\ \\ \sf{2 {y}^{2} - 5y + 10 = 0} \\ \sf{Comparing \:with \: a {x}^{2} + bx + c = 0 , \: we \: get \: \: ,} \\\sf{ a = 2, \: b = - 5, \: c = 10} \\ \\ \sf{ \: \: \: \: Δ = {b}^{2} - 4 \: a \: c} \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Δ = { \: (- 5)}^{2} -4 \times 2 \times 10} \\ \sf{Δ = 25 - 80 } \\ \sf{Δ = -55 \: \: \: \: \: \: }$