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secondary 3 | A Maths

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please help with parts (b) and (c), apparently simultaneous method is needed to solve these. any help would be greatly appreciated!

(3-x)²+2 = x²-6x+11

Δ = 36-4×11 <0

∴ there is NO x-interception with x-axis

ans is 0

x² - px + (p-1)

Δ = p² - 4(p-1) = p² - 4p+4 = (p-2)² >0

∴ there is 2 x-interception points with x-axis

ans is 2

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